Madonna and the Hyperbolic Manifold

Visual Mathematics in Paintings by Da Vinci

In the Madonna and the Yarnwinder, the Virgin Mary tries to restrain her child from the yarnwinder, which represents the Passion of Christ; or the Cross. You may have noticed that the trancepts of the yarnwinder are not completely parallel, and were they to be extended they would meet at some point to the left hand-side of the image. For two parallel lines to meet in this manner, mathematicians suggests that space would need to have a constant positive curvature.

 The Madonna and the Yarnwinder earned its creator, Leonardo Da Vinci, the title of ‘the slowest painter in Italy.’ Anyone of his compatriots would have been able to complete a painting of similar size, and content, in a matter of months, and yet it took Leonardo four years to complete Madonna and the Yarnwinder. Why? It has been suggested that Leonardo was constantly thinking about something grander than merely the task at hand, and that his commissions suffered from this lack of focus accordingly. Be that as it may, the bizaare fault in the logic of the perspective of the yarnwinder could not have been overlooked by Da Vinci, in the four years he spent working on this project, and therefore must be considered deliberate.

Rhombicuboctahedron by Leonardo Da Vinci, and Waterfall by MC Escher.

Only one thing could account for the disparity in perspective, and the length of time it took Leonardo to finish the relatively small and simple composition; the impossible triangle or tribar. Unfortunately, it was not discovered until some 400 years after Leonardo’s death. It is well known that Leonardo was able to render perfectly symmetrical 3D politropes onto 2D surfaces with apparent ease. For this reason I think it is possible that he may have come up with the tribar, a projection of a 4D object onto a 2D surface. The tribar, was first created by the Swedish artist Oscar Reutersvard in 1934. It was independantly devised and popularised by Roger Penrose in the 1950’s, who studied it from a maths perspective. MC Escher is considered the first artist to render these mathematical concepts in a graphic medium. His visions of strange worlds, where the laws of gravity seem to no longer apply, are the result of this study. Considering that the tribar was initially discovered by a graphic artist, and later expounded upon by one, it is not so difficult to concieve that Leonardo Da Vinci could have come up with his own version of the object, much earlier.

The tribar is known as an impossible object because it cannot be physically realized in 3-d space. However, it is possible to generate a tribar in some types of 3-manifolds (hyperbolic types). Manifolds are essentially surfaces. Topology describes the surface of a sphere locally, as a 2-d or 2-manifold that encloses a 3-dimensional space. Similarly, a 3-manifold is a 3-dimensional space that is locally 3-dimensional but extends to enclose a 4D space. It is possible to create an approximation of an impossible tribar in 3-d space, either by creating a disjointed or curved representation of it that appears to be coherent or connected from one particular angle. In the instant of the curved model, a number of different varieties can be considered. I prefer my own solution which requires one of the arms of the tribar to be negatively curved, one to be positively curved and the conjoining one to be bent in an S-shape; comprising both positive and negative curvations. Of course, from the point of view of the 3-manifold/4-dimensional object no curvature in any of the arms of the tribar would be necessary.

In order to prove that Leonardo incorporated the mathematics of the tribar into Madonna and the Yarnwinder it will be necessary to distort the appropriate areas of the canvas by these degrees of positive and negative curvature – something that would have been almost impossible to do before the advent of image manipulating software like Photoshop. According to my calculations, the optimum amount of tribar curvature should be plus or minus 32%. After spending many hours on the resulting animation, I got the feeling that I was completing one of Leonardo Da Vinci’s unsung, and unfinished works. It is possible that the visionary who foresaw such marvels, as the submarine, helicopter and animatronic android, could have envisioned the Computer Age, when his images could be stored, recreated and manipulated with comparitive ease. In such an eventuality, I felt I had become almost like the distant understudy of Da Vinci, playing my part in the completion of a masterpiece that took, not just four years, but four hundred to be fully realised.

On the face of it, it does appear as if these tribar based distortions reveal Leonardo’s true intentions where this painting is concerned. Watch, as the head of the Madonna begins to shrink into a more proportioned stance with her body. Watch, as vistas are partially occluded by mountainous terrains, and bodies gesture in life like motions. Could this be the first Renaissance painting to include a code that unlocks a 3-dimensional perspective within its coloured forms? If it is, then, it is the only one that I known of. The entire landscape appears to be alive and breathing with an innate lifeforce. The snowcapped mountains of the background behave like teeth being pressed, from behind, by giant emerging molars of wisdom. This is Renaissance painting on LSD.

It is my belief that the dimensional permutations of this animation focus the mind and permit consciousness expansion. For this reason, I urge you to watch its endless looping permutations for 1 and a half hours (if you can!), for two days, at the end of which time, your brain should be sufficiently conditioned to produce the desired effect without the aid of the animation to help you. The effect is similar to that which you can find in some of those maddening optical illusions, but it is far more dynamic and rewarding, I assure you. Far more interesting, is the impact it has upon your dreams when you sleep!

EndlessVideo - yarnwinder2.mov

In the process of contructing this animation, I wound up watching it for hours on end, and noticed some very pleasing results. The piles of clothes littering my bedroom floor began to warp and wiff in the same manner as the painting. When I went out onto the landing of my country home, and tried to walk around in the dark, the angles of the walls began to rotate and distort wildely. They appeared to have more freedom of movement, which presented the possibilty of corridors opening up, where previously there were none. This is the effect of inter-dimensional code embedded in Madonna and the Yarnwinder, a dislocation of the mind from the 3-dimensional temporal sphere.

Considering the minute comparisons between the LSD experience and the effects of watching this video, it should not come as too much of a shock that such temporal distortions should occur. After all, the secret governmental agencies of the world have been experimenting with the combined use of LSD and time travel for decades. See here; and stay tuned for more on that subject later.

Serpentine Dream Theory

In the 2007 movie Southland Tales a group of public figures comprised of actors and porn stars, are indoctrinated into a secret research project known as Serpentine Dream Theory (SDT) - not to be confused with STDs. The project involves hypnotism, time travel and the habitual use of an organic component known as Fluid Karma. As stated before, Fluid Karma is a highly psychoactive compound that has much in common with the hallucinogen DMT. Robert Frost refers to cacti in his seminal poem The Hollow Men, as a means to describe the sterility of modern America.

Here we go round the prickly pear.

However to dance around any plant is to give homage to it. No cactus is perhaps more deserving of praise, in this manner, than that of the peyote cactus. Peyote is prized for its natural production of mescaline. Mescaline is a psychotropic compound with effects similar to that of DMT and the fictional drug Fluid Karma. Medea, the Greek heroine, skilled in the craft of vision inducing substances was schooled by Hecate. Hecate, the Goddess of witches and crossroads, is associated with the Fluid Karma project. The SDT project is a highly convoluted affair. Participants are drugged, flown through a rift in timespace, hypnotised and then encouraged to continue the use of the organic compound drug Fluid Karma. The combination of these three conditions grants the unwitting participant the ability to see into the past and the future; a property associated with the Goddess Hecate herself.

The application of LSD in US governmental programs such as MK-ULTRA is well documented. But its use in the research of time-travel is less well-known. One source, that could be described as dubious, is the testimony of Preston P. Nichols, who was an engineer for the shadowy Montauk Project. Montauk was a secret research program allegedly involved in a plethora of black operations such as; material manifestation, teleportation, time-travel, alien conspiracies and mind control/manipulation. Preston claimed that special rooms were provided for candidates to experience psychotropically altered states of consciousness; with a special regard for the remote viewing of different time spheres. The rooms were decorated in a variety of psychedelic wallpaper and their dilapidated ruins are apparently still accessible on the now defunct Montauk AFB.

A number of years ago, I was told a story by a friend of mine who had an acquaintance with a guy named Paul - not his real name. As a child, this acquaintance befriended a boy, called Rick, also not his real name, who lived in a house across the street. As they grew older, they grew apart; a state of affairs familiar to most people. In later life Paul became involved in the Dublin drug scene and gave little thought to what had become of his old friend. During this time Paul was admitted to hospital after ingesting a large quantity of LSD. His trip was of epic proportions; involving a fight for his soul between the Devil, on one hand, and a legion of angels on the other. While he was recuperating in hospital he received a visitor, which turned out to be none other than his old childhood friend Rick. It transpired that  Rick had enlisted with the British Secret Services following emigration to the UK. This did not strike Paul as unusual, as Rick had always shown a keen interest in the military growing up. After a brief conversation, Rick invited Paul to take a questionnaire that might shed light on his LSD experience. Paul agreed, and was surprised when filling out the form to encounter questions that related specifically to time-travel.

What this story tells us is that, far from being considered in a skeptical manner, time-travel is of particular interest to governmental agencies. Not only that, but it is apparent that they believe strong hallucinogens can permit ordinary citizens to foresee temporal events that are beyond the call of major analysts. These conclusions should not really be all that surprising, considering the unique advantage knowledge of the future would bring to a covert war. We should also consider the ongoing efforts of different governmental agencies in the prediction and control of the future. These efforts may take unusual forms, and may explain some of the time travel codes that have appeared in connection with 9/11 and other more recent events. I have already shown connections between the 911 Solar Ritual and the time travel plot of Southland Tales. Of course this plot is not restricted to Richard Kelly's creations and, as I have shown, reaches into the world of show business and space travel; two disciplines that have become more closely intertwined than ever before, in recent months. It appears MI5 may have learned from the mistakes of the CIA and MK-Ultra, when it comes to finding test subjects for their experiments. Instead of drugging people against their will, they merely wait for the inevitable OD patient to be admitted to the hospital yards. This provides the valuable information that they require, without running the risk of causing a public outcry.

So, Richard Kelly's narrative, of a group of shadowy figures drugging and hypnotizing familiar personages in the hope of finding out more about the future, is not as far-fetched as it might, at first, appear. It would, to my mind, be extremely gratifying to get a look at the questionnaire Paul, allegedly, underwent. The Serpentine Dream Theory is connected to a much larger project called the Doomsday Scenario Interface (DSI). Fictional within the confines of Southland Tales, this project might find realistic comparison with the Y2K and 911 false flag and non-starter operations. These two massive projects might be part of a government operation to research, in advance, the possibility of an actual cataclysm occurring in 2012. On the other hand, the fear inducing propaganda surrounding these events, may trigger an unprecedented ability within the general populace to predict and offset undesirable futures for themselves. The symbol for the DSI occurs as a subliminal message in the movie ST, due to an editorially advised cut in the length of the film. The symbol for the DSI is reminiscent of the Antinomial Sigil of the TOPH, a Satanic organization connected to Aleister Crowely and the worship of the demon-begetter Lilith.

Antinomianism is the theological belief that members of a particular religion are under no obligation to follow rules of ethics or morality, given that salvation is by predestination only. Antinomianism, by its definition, omits the intervention of an omnipotent God, in favour of a predetermined timeline. It is, therefore, no wonder these people would be so interested in time travel, because such abilities would give them the power to alter their own destiny, and the destinies of those around them. Perhaps the infamous internet-based time traveller John Titor was correct when he said that the Large Hadron Collider would open up new avenues for research into time travel. And perhaps it is no accident if it does so.

Serpentine Dream Theory may have found its precursor in the Dragon Project Trust (DPT). The DPT was founded in 1977 to investigate claims that prehistoric sites have unusual forces or energies associated with them. In the end, the DPT became a 'dreamwork program' that 'is a kind of modern revisiting of the ancient practice of temple sleep (see Divination).' The program was jointly conducted with the Saybrook Institute in San Francisco and, ultimately, determined its findings by means of the Strauch Scale. Like the Serpentine Dream Theory, the Dragon Trust is interested in divining knowledge of another time by interfacing with the unconscious human dream state. Serpentine describes dragons.

The Saybrook Institute has something of a history in the analysis of psychic visions and dreams. In 1970 Eva Hellstrom (Hellstorm?) posted a notebook consisting of 21 of her reported dreams and 45 of her reported visions - 66 in total - to Stanley Krippner at the Saybrook Institute. The Strauch Scale was applied to these dreams also. The name Eva Hellstrom is qualitively similar, in my mind, to Dr. Inga von Westphalen - the name of one of the scientists in the Southland. Von Westphalen was the one who brought the tempest to the Southland. The tempest was embodied by her son, the Baron von Westphalen, who also symbolized the Beast of Revelations. And so, by the pricking of my thumb, a Hell-storm in the West - has - fallen. Somewhat coincidentally, in Ireland at the moment the entire Shannon River, the largest in Western Europe, is in flood.