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Heavy Circle = Hypersphere (Glome), Lighter Circles = Azimuthal Circles
Vertical Line from centre = Glome antipode distance L, let d = astronomical distance/L.
Horizontals = Glome radii = sqrt(d-d^2)
Hypotenuses = Azimuthal radii = = sqrt(d^2 + (d -d^2))
*Hypotenuses/Horizontals = sqrt(d^2 + (d-d^2)) /sqrt(d-d^2)
*This ratio submits to the following simplification
or to
where d now means simply the astronomical distance, as A = c^2/L.
Dividing the two gives the ratio of Azimuthal radius to internal Glome radius so the ‘Lensing’ shown means the degree to which the object under observation at some distance d/L gets ‘spread out’, suggesting that we could multiply this by the standard factor for reduction of brightness with distance of 4pir^2
Explanation: Glomes (3-spheres or 4-balls) have an unobservable 4th dimensional radius of curvature.
The vertical axis represents the real distance to L, but along it every point d on it has a corresponding point on the unobservable 4th dimension axis corresponding to sqrt(d-d^2) for its unobservable radius of 4th dimensional Glome curvature, and to sqrt(d^2 +(d-d^2)) for its unobservable radius of 4th dimensional Azimuthal curvature.
The ratio of these unobservable sqrt(d^2 +(d-d^2)) / sqrt(d-d^2), gives a third unobservable sqrt(1/(1-d)), which we can render into an observable by multiplying it by the expected drop off in brightness for distance d.
Prediction: The curve begins with a gentle almost flat slope, and this looks, the same as the results obtained for the type 1A supernovae. On the basis of the angle of the slope the Hubble constant became adjusted and the assumption of dark energy became adopted.
However, we cannot easily observe type 1As at huge distances, and the curve turns from a gentle slope into a steep curve at huge distances.
This hypothesis therefore predicts that at huge distances the dimming will become much more acute and that dark energy does not exist.
Horizontal scale distance, Observer to antipode L.
Vertical scale, for red and blue lines, the unobservable 4th dimension of curvature radius. Green = hyperspherical lensing, corresponding to the increasing observed magnitude with distance d.
Interpretation: This hypothesis forms part of the Hypersphere Cosmology hypothesis which models the universe as a Vorticitating (4-rotating) Hypersphere (Glome) which will appear to inside observers in Azimuthal Projection. This hypothesis also eliminates singularities, the big bang, inflation, and dark matter.
The treatment of gravity / spacetime curvature as a 4th dimension orthogonal to three-dimensional space and to time implies the non-quantisation of gravity and suggests that unification may lie in the geometrication of the quanta, perhaps in higher dimensions.
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A Glome in Azimuth.
Since humanity first gazed up at the stars we have wondered - how big a universe do we inhabit and what shape does it have? Does it have infinite extension in space and time, or does it have boundaries, and if it has boundaries what lies beyond them?
In the twentieth century we reached several consensus conclusions by interpreting newly available data provided by powerful telescopes of various kinds, including those that could ‘see’ forms of light and radiation that our eyes cannot detect.
Some of these consensus conclusions remain questionable.
The universe appears vastly larger than we previously thought. As light travels at a constant 300,000 kilometres per second then the furthest detectable sources of it seem to lie further than 10 billion light years away from us and the light from them has travelled towards us for as many billions of years. There seems little doubt that we inhabit a very large universe with very long history.
Around 1930 a consensus developed amongst cosmologists that the universe has expanded continuously from an initial condition of having no size at all, and that the sources of light we can observe at extreme distances now lie much further away than ten billion light years. The consensus theory of a universe expanding continuously from a ‘Big Bang’ has dominated cosmological thinking for nearly ninety years but it has led to utter confusion and the multiplication of a swathe of questionable sub-hypotheses which attempt to prop it up, such as singularities, cosmic inflation, dark matter, and dark energy. These sub-hypotheses complicate estimates of the age and size of the universe. The current consensus guess puts the supposed big bang about 13.8 billion years ago.
This paper considers proposition that the universe does not expand and that it has a shape in space and time quite different from what the expansion hypothesis suggests.
The Hypersphere Cosmology articles and papers on this site show how we can quite easily avoid the phlogiston like ‘phenomena’ of singularity, inflation, dark matter, and dark energy by simply dropping the expansion hypothesis and describing the universe as a Vorticitating Hypersphere finite but unbounded in both space and time. In this model the phenomena conventionally explained by the presence of dark matter (galactic rotation curves) and dark energy (an unexpected dimming of very distant sources) all arise as a direct consequence of the geometry of the hypersphere.
‘Hypersphere’ can refer to any form of sphere that has more than three dimensions, in Hypersphere Cosmology it refers specifically to a geometry that mathematicians describe as a 3-sphere or a 4-ball, it also has a particular name – a Glome.
So, if we inhabit a Glome, what shape will it appear to have to us observers inside it?
Because light itself follows the gravitational curvature of space (and a Glome curves back in on itself due to its gravity) we will see the universe in Azimuthal Projection.
(The Azimuthal Projection creates the optical illusion of spreading out and dimming light from very far sources, the model does not require dark energy to explain that.)
We can visualise Azimuthal Projection fairly easily. Imagine that you stood on the north pole of the earth but that the earth had such immensely powerful gravity that light could only travel around its surface. From the north pole you would see the equator as a circle surrounding you because light would travel around the curve of its surface. If you looked further you would see the south pole in very direction around you, stretched faintly around the entire horizon. It would look like this because we always assume that light travels in a ‘straight line’.
See this Azimuthal Projection of the earth for an observer at the north pole.
Now in three dimensions something analogous occurs if the gravity of the system (the spacetime curvature) has the strength to bend light right around it. You will see the antipode (the point at the opposite side of the universe to you) spread out faintly as a complete spherical surface surrounding you, billions of light years away.
(You might think that at twice that distance you could theoretically see yourself, but the spacetime curvature redshifts light to oblivion beyond antipode distance.)
So, on the basis that we inhabit a Glome in Azimuth, my astronomer/cosmologist friend and I now seek the precise equation for the unexpected diminution of luminosity at extreme distances which will kill the dark energy hypothesis and put the final nail into the coffin of the Lambda-CDM model and all other variants of Big Bang theory.
Einstein got it more or less right the first time, he should never have listened to Lemaitre.
Spring Equinox.
As the autumnalis Mandrakes in the greenhouse prepare for their summer hibernation and their leaves begin to yellow, the frogs and toads move into the pond at Chateaux Chaos and the flowerbeds begin their slow magnificent explosions. Everything seems a bit early this year after the unseasonably warm February.
My attempt to fashion a mermaid from concrete over scrap steel and wire using rather stochastic procedures, (whatever comes to hand and mind), seems to evolve towards an image of Sabrina, the bountiful but fierce goddess of the nearby River Severn. Or does she look like Britannia with that trident?
Brexit seems to hang in the balance. Will we finally summon the resolve to exit the perfidious undemocratic synarchy that the EU has become, or will the self-interest of the euro-political class and big business triumph and intimidate the electorate into accepting a partial Brexit fudge or no Brexit at all?
Good fences make good neighbours as they say, but they become even more essential when you haven’t got particularly good neighbours. If we had not got duped into joining the EU, we would certainly not want to try joining it now.
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I received an invitation to write a piece for publication in Japanese in a Japanese journal of Magic. I present it here in English.
The Way of the Wand.
Religion seeks knowledge and power through the understanding of the will of Supernatural Agencies.
Science seeks knowledge and power through the understanding of Natural Mechanisms.
Magic seeks knowledge and power through the understanding of Intents – personal intents, the intents of others, and the intents of natural phenomena.
On a superficial level, all three disciplines loathe and despise each other. Scientists dismiss the existence of supernatural agencies and the existence of intents (including free-will). Religionists loathe and despise the reductionism of scientists and regard the hubris of magicians as evil and blasphemous. Magicians consider science incomplete and regard all religious ideas as rather arbitrary vehicles for Intent.
Many people who express an interest in Magic only really want the consolations of religion and mysticism and something ‘spiritual’ - whatever that may mean.
If spirituality means ‘the way you live your life’ then Magic certainly has its own ‘spirituality’ – ‘Living your life by Intent’ - making things happen by all available means.
We should not confuse Intent with ‘willpower’ as in some early 20th century definitions of Magic. Both willpower and Intent arise from Imagination. The capacity to imagine what you want, consciously and subconsciously, and the imagination to build on that to the exclusion of other needs and wants and fears and distractions, leads to the knowledge and the power of Intent.
One thing marks out Magicians from the Scientists and the Religiously inclined. Magicians constantly practice Enchantment; they cast spells all the time. They may also practise Divination, the attempt to divine the intentions of people and events, or Invocation, the attempt to draw inspiration from imaginary supernatural agencies or their own sub-consciousnesses, or Evocation, the attempt to control the intent of imaginary supernatural agencies or their own sub-consciousnesses, but Enchantment remains the defining activity of a Magician.
For this reason, effective magical training programs always start with Enchantment and the use of wands and spells and sigils. Only those who truly ‘pick up the wand and run with it’ will ever master the life skill of Magical Intent. The rest will just end up toying with tarot cards and the like and creating their own idiosyncratic mysticisms and religions.
A Magician can do Enchantment without a literal physical magic wand, in the same way that anyone can do simple carpentry with their bare hands by breaking and twisting small pieces of wood together, but precision instruments give better results.
As the traditional instrument of Enchantment, the Wand serves several purposes; the magician can use it to focus more intently when drawing spells and sigils in the air, or in the mind’s eyes of imagination and visualisation. Wands also serve to constantly remind Magicians of their chosen vocation to Live their lives by Intent, whatever the distractions and blandishments and fears and conventions of contemporary life.
A Magician should always make Wands that represent personal intents and meanings. Two Wands will often suffice, a large one in the form of a staff of the Magician’s own height for use in private or special places, and a smaller pocket wand for carrying always. Magicians should consider upgrading their wands continuously during their careers as their skills and knowledge and intents develop.
A Wand does not even have to look like a conventional Wizard’s wand. Some Magicians have successfully defined special objects in the shape of rings or amulets or even weapons as their Wands.
Magic does not always work, but on the other hand Religious appeals to supernatural agencies work even less well, and Science frequently fails to do what we want it to because we inhabit a universe with a lot of randomness in it. This randomness has two consequences for the Magician, it makes Enchantment possible, but it also renders Divination subject to probability.
If only a fifth of your spells work or you find that you can only achieve a twenty percent distortion of probability, then you still have a real power that with persistent and subtle application will yield good results. If, however only a fifth of your Divinations give the correct answer then you will acquire a disability if you act upon them.
Additionally, because of the existence of randomness and probability, Enchantments work best when aimed well into the future whilst Divination gives better results over shorter times, so as I always say, whenever possible - ‘Enchant Long and Divine Short’. Of course, Magicians would prefer to Enchant and get a result quickly and to have the ability to Divine the distant future, but the chaos and randomness in this universe which makes Enchantment possible makes these acts difficult.
Taking the Way of The Wand means living in a universe of Intents and challenging yourself to succeed at difficult activities that require some sensitivity to the Intents of others and the Intents of human made systems and the Intents of physical reality, as well as a quiet self-confidence and a well disguised supreme arrogance.
Magicians rarely succeed in working together for long. Rivalry tends to become enmity. Magic tends to become a solitary pursuit shared only through books and manuscripts and letters. Humans tend to revile or ridicule or fear those who advertise themselves as Magicians in Science based cultures, and in monotheist Religious cultures, and not all Pagan cultures have regarded it favourably. Magic thus tends toward discretion if not outright secrecy.
Nevertheless, many magicians smile quietly when they notice ordinary people inadvertently using magical thinking quite successfully. Belief in the power of Intent and belief that all phenomena have Intents does often give good results, even if Science believes otherwise and denies even human free will. Believing in Intent seems an indispensable element in the human toolkit but use it with care and with a carefully crafted Wand for best effect.
Ordinary people seem to recognise the power of Intent but so often see to shy away from it out of fear about where it might lead them. It does have its dangers, but the Magician decides To Know, To Imagine, To Dare, and To Keep Silent.
A correction to all versions of Hypersphere Cosmology.
Since I started collaborating with a gamma-ray astronomer on the Hypersphere Cosmology hypothesis we have started checking the math in fine detail. The precise formula for redshift appears below, previous versions gave only its square root.
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Vulcan-ology.
Dion Fortune always said that magicians should acquire varied craft skills. Retirement from commerce allows me to explore some grander projects I’ve always wanted to have a go at, so in addition to working on a life-size concrete over wire Mermaid/Britannia to sit by the ponds, I took a days course in Blacksmithing with the brilliant Artist Blacksmith Joanna Williams www.fireironart.com after a few practise pieces I tried making some pocket wands using various hammering and twisting techniques to create ‘water twists’ and ‘pineapple twists’ to suitable effect.
In the past I tried welding a couple of times and didn’t enjoy it much with all the thick tinted goggles and visors and hot metal spattering, and arc welding proved even less fun, but Blacksmithing proved a joy I hope to repeat. There seems something so very elemental and historic about getting in there with fire and water and air to forge metal from the earth with hammer and tongs. Io Vulcan!
Magic and Physics News.
No real deep difference exists between these two subjects, they inform, rival, and complement each other. Physicists rebel against Magic, and ‘A Witch is a rebel in Physics’ as Thomas Vaughn observed. Both disciplines seek the knowledge and ability to understand and manipulate reality. Physics models reality in terms of Mechanism, Magic models reality in terms of Intent. The Mechanisms of any phenomena, from ourselfs to all things in material reality, equate to their Intents.
Arcanorium College has just welcomed Chaos Magicians and Physicists from Japan. The Japanese Chaos Magicians have a considerable active history which we in the west have remained largely unaware of until now.
Arcanorium’s ‘One Wand Three Spells’ course provoked some very inventive wand design and results of spells continue to come in.
This continues to attract attention http://vixra.org/abs/1812.0155 and a recently established collaboration with a gamma-ray astronomer will hopefully led to some testable predictions for publication.
The hypothesis of Hypersphere Vorticitation continues to draw questions about how exactly do galaxies move around the cosmos. An exact visualisation of 4-rotation proves challenging, but the ‘Hopf Keyring’ provides a reasonable analogue. The galaxies rotate around orbits corresponding to the rings, all orbits pass within all the other orbits. Thus, although all objects move to their antipode positions over a period corresponding to the Hubble Time, objects close to an observer’s antipode will appear to have a lateral motion of a tiny fraction of an arcsecond per century.
Deja-Review.
It proves very annoying to become mis-quoted or to write a manuscript review and find it edited in a misleading fashion. For this reason, the review appears here in its entirety - a fair and polite review of a rather pedestrian book which contains almost nothing new.
Hi Daniel, herewith my review. Perhaps you would care to add my Liber Null and Psychonaut to the bibliography. (He didn’t)
Shamanic Qabalah by Daniel Moler provides an in-depth guide to the esoteric ideas and practices at the core of the magical revival in the western mystery tradition that began in the late 19th century. An earlier revival took place in the first two centuries AD in the form of Gnosticism, Hermeticism and Kabala, and these have heavily influenced western esoterics since their revival in the 1880s.
Moler points out that Shamanism represents the original wellspring from which all mystical and magical traditions around the world originate, and he integrates his extensive personal knowledge and experience of Native Andean Shamanism with his equally extensive knowledge and experience of the Western Magical Tradition to re-enliven the latter, to make it more accessible and less seemingly scholastic, and to add back a bit of the old shamanic and passion and fire to it, and to give it a social and ecological conscience as well.
Moler sidesteps the Neo-Paganism and Chaoism of the late 20th century revival and develops the Platonic Pagan-Monotheism of the first and second century revival and the late 19th century revival into a Pantheism with strong spiritual and psychological theme which seems destined to find its niche in the dynamic spiritual marketplace of the 21st century. Peter J Carroll.
On opening the Moler’s book this truncated sentence becomes the very first thing you see: -
Shamanic Qabalah by Daniel Moler provides an in-depth guide to the esoteric ideas and practices at the core of the magical revival in the western mystery tradition. Peter Carroll.
Either Moler or Llewellyn publishers have responsibility for this misrepresentation, stick with respectable publishers.
Academia. The following may amuse: - https://www.academia.edu/35746068/The_Illuminates_of_Thanateros_and_the_Institutionalisation_of_Religious_Individualisation_preprint_
One for the archive.
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With retirement from the distracting task of making a moderate fortune, a little more time has become available to concentrate on other significant quests: -
Cosmology. Herewith Hypersphere Cosmology 3. Compressed down to just 3 pages from the 30 or so pages of the hypotheses that make it up, it provides a brief and scientifically/autistically terse summary of the central arguments and mathematics. Mysteriously post-dated.
http://vixra.org/abs/1812.0155
Magic. Herewith the new Chaobala Pocket Wand Mk13, somewhat in the style of a Tibetan Dorje/Purba crossed with an Olympian Thunderbolt. It has facets for the major archetypes of the Epoch Chaobala, a cubic pommel for the Classical Elements surmounted by a pyramid for Aether, a central Octagonal section for the Octaris with numbered god forms, and a Pentagonal point for the Elder Gods of the Cthulhu Mythos.
Handcarved from a bar of solid element 13 (Aluminium, dedicated to Ouranos). Stable up to over 6000C it should survive even the most challenging conjurations.
New Courses & Facilities on Arcanorium starting December 2018 and January 2019.
The Classical Elements. A Magical Theory course; - The ideas of Empedocles about Earth Air, Fire, and Water have informed the esoteric arts for two and a half millennia. Can we still find some use and meaning in them? Taking Classical, Medieval Renaissance, and Modern sources and the Neoplatonic Chocolate Screwdriver from Specularium and Liber 555 from The Epoch as starting materials we shall see if we can forge onwards from there.
Problems and Challenges A Problem-Solving Facility. A Forum where participants can present their own and the methods they use to solve them magically. This provides a forum for feedback and suggestions, and secondly will provide an archive of case histories of strategies and tactics that did and did not work.
Finding Cups -Seeking Divination & Apophenia in the Environment. A Practical Magic course: - Using the World itself as a scrying instrument. With special contributions from Frater JayO from the coast of British Columbia.
The Magical Link. A Magical Theory and Practise course: - Here we look at one of the trickiest and most problematical aspects of magic – how to establish functioning links across space and time between magician and target in both Enchantment and Divination. Starting January, with special contributions from Frater Hannes of Austria.