Arcanorium CollegeCollege News and Views

Pete Carroll

Wednesday, 28 January 2015 15:36

Review and Philosophy.

Dave Lee writes his long awaited and very thorough Review of Epoch

Thanks Dave.

And now for some philosophical musings.

The Philosophical Implications of Hypersphere Cosmology.

Philosophers have long wondered whether the Universe has finite or potentially infinite or actually infinite extension in space and in time.

In the case of finite extension, the question has naturally arisen of what lies beyond it, or what, if anything, ‘contains’ the Universe.

Philosophers have generally regarded space as a Privative Concept rather than a positive concept, and considered space to consist of the absence of things, a nothingness which can accommodate the presence of various phenomena and objects.

Thus a spatially finite universe could, for some philosophers, simply exist within an unlimited space of pure nothingness, but unlimited nothingness means very little except perhaps for the potential for events to happen there.

A Universe consisting of an infinite amount of phenomena and objects spread over an equally infinite amount of space seems a tricky concept. We can say it, but we cannot really visualise it, and many would argue that the concept of infinity can have no physical correlate and that the concept only arises when we take the mistaken course of dividing by zero, or by assuming infinite divisibility, or of assuming that some other quantity has an infinite value. Yet if any quantity has an infinite value then all quantities must have an infinite value. A truly infinite universe would presumably contain an infinite number of stars, an infinite number of earth like planets and an infinite number of creatures including an infinite number of creatures exactly the same as each individual one of us, and an ‘equally’ infinite number of near copies.

Philosophers have also long wondered whether the universe has a finite or a potentially infinite or an actually infinite extension in time, and some have wondered if time itself might have some vast eternal circularity to it, or even to have a purely illusory nature.

Time can to some extent have the appearance of a Privative Concept like empty space, an absence or nothingness which awaits events to fill it up.

The nature of time becomes mysterious in proportion to the amount of thinking devoted to it, yet for any observer, events do seem to have a sequence, some things happen before and some things happen after, that much seems unarguable, and from it we abstract the idea that some form of cause and effect, with the cause preceding the effect, often applies. Even if some observers disagree with others about the order, and some effects appear random, or occasionally retroactive, or magical and occult, the universe broadly seems to go through sequences of events in time, everything obviously doesn’t happen simultaneously.

We can only measure time by movement and change. Potentially infinite time or actually infinite time only has any meaning if some sort of movement or change exists to delineate it.

If absolutely everything in the entire universe stopped moving, right down to the subatomic level, and then started moving again, ‘the amount of time for which it stopped moving’ would remain undetectable and without any effect whatsoever, it would have no reality.

Despite that most of our measures of time have an element of circularity about them; the cycles of night and day, the days of the year, the seemingly endless human cycles of birth and death, the movements of clocks and ultimately the vibrations of atoms in our most reliable timekeeping devices; we also have linear views of time in which many things have a beginning and an end. Even a clock does not exhibit perpetual eternal recurrence; it requires assembly and it will eventually break.

Most monotheist and some pagan religions view the world in terms of a linear timeframe with  deities initiating beginning, a middle, and some sort of apocalyptic and/or transcendental ending, and of course most of them regard the universe as limited in space, often vastly more limited than even the simplest astronomical observations now suggest.

The Privative views of space and time do not now seem sustainable since the advent of General Relativity.

 Newton considered that space provided some sort of fixed absolute immutable void in which objects could exist and that time provided some sort of constant immutable flow in which objects could change. However, most crucially, the objects within space and time could did not affect the space and time.

‘Absolute space, in its own nature, without regard to anything external, remains always similar and immovable.’


‘Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external,’

Einstein’s General Relativity however shows us that the presence of any object; mass or energy, does profoundly affect the properties of space and time. We can no longer consider space and time as voids which can contain events. Space and time have a structure which depends on the presence of mass and energy.

Einstein realised that: - ‘Matter (and energy) tells spacetime how to curve, and curved spacetime tells matter (and energy) how to move.’

Thus gravity does not exist as a ‘force’. Mass and energy give rise to curved spacetime, (that we commonly recognise as gravity) and conversely, spacetime curvature gives rise to mass and energy. None of these phenomena exists independently of the others.

Truly empty space does not exist, it always has some kind of curvature or gravity in it, and the rate at which time ‘flows’ depends on the curvature also.

Einstein’s General Relativity modifies the Newtonian model of gravity under conditions of strong gravity; the Newtonian model remains valid as an approximation where the gravity remains fairly weak. Hypersphere theory modifies General Relativity for the conditions of very strong gravity where the spacetime curvature distorts Euclidian spacetime so much that it adopts a hyperspherical configuration which rotates. This occurs on the scale of the universe itself, almost certainly inside black holes, and rather surprisingly perhaps, in fundamental particles. Hypersphere theory also suggests that the geometry of time matches that of space, and that time has three dimensions rather than one.

For any three dimensional body of roughly uniform density the spacetime curvature increases not by its length but by the cube of its length. Thus the universe cannot consist of a more or less large scale uniform density body of infinite extent, for if it did then the spacetime curvature within it would become infinite as well, time would stop and light could not travel.

In Hypersphere Cosmology the universe has a ‘Finite and Constant’ but ‘Unbounded’ extent in both space and time.

The surface of the Earth has finite and constant but unbounded extent, you can travel as far around it as you like without encountering a boundary or an edge to fall off. Every point on the Earth’s surface also has an antipode point, the point on the other side of the world which represents the furthest away from your starting point that you can get.

Now the entire universe has a similar sort of spatial geometry but in three rather than two dimensions. You could, with a good enough spaceship and plenty of time, travel about 13 billion light years in any direction and eventually reach the furthest point away from your starting point that you could ever reach because the vast gravity of the universe causes it to curve back in on itself at that scale. If you attempted to carry on traveling you would eventually end up back where you started. However as nothing can travel faster than light this return journey would take at least 26 billion years, by which time your starting point would have few recognisable features left. Your home planet and star would probably have ceased to exist and your galaxy would have probably moved a fair distance and changed shape.

The ‘temporal geometry’ of the hyperspherical universe works in a similar way, the vast gravity of the entire universe curves time back in on itself, thus no event will appear to have occurred further away in time than about 13 billion years because the light from it will have become redshifted out of existence. However if you could somehow wait for 13 billion years you would not see the same events unfolding again, in the same way that travelling for 13 billion light years would not bring you back to anything like the ‘same’ place. Nevertheless in theory something like an ingot of tungsten drifting in deep intergalactic space could in principle persist for much longer than 13 billion years so long as a star in a passing galaxy did not suck it in, or cosmic radiation did not gradually erode it.

Hyperspheres rather than singularities will form within black holes, but no matter how much mass they absorb they will not change the overall size of the universe. Even if all matter in the universe falls into hyperspheres and the hyperspheres coalesce into each other that merely leaves the universe as a single hypersphere at the same size.

Hyperspheres with three spatial dimensions necessarily exist embedded within a spatial manifold of four dimensions, much as the curved two dimensional surface of the Earth exists only in the context of three dimensional space. We can of course dig holes some way into the planet, get some short way up into the sky or with enormous effort get a short distance into space. Unfortunately the fourth spatial dimension of a hyperspherical universe does not appear to offer any extra-dimensional travel freedom because the three dimensional space fills it up entirely, it has the same scale.

Philosophically, a universe finite and constant but unbounded in space and time leads to a rather different view of humanities place in it, to the views arising from either an infinite universe or from a universe with a beginning and an end.

A universe with a beginning and an end fits the Judaeo-Christian monotheist model and also some pagan models like the Norse one which ends with a cataclysmic Ragnarok. The final conditions implied by these philosophies suggest either historical or personal lifetime progress towards some kind of transcendence, or stoical endurance till final oblivion.

Some oriental philosophies like Buddhism and Hinduism seem to mainly take an eternalist view of the universe, cycles of creation and destruction, birth, death, and reincarnation go on endlessly with no apparently beginning or ending in sight. Such philosophies can often seem to promote a certain resignation to fate.

A hyperspherical universe, finite but unbounded in space and time, perhaps suggests other philosophical views. Finiteness has become impressed upon us by the pictures of our planet from space and the growing recognition that it cannot supply us with unlimited or infinite resources, we can go around its unbounded surface as far as we like, but we cannot go any further; we will probably have to put up with this for the lifetime of our species, for space travel will forever remain unrealistic unless fundamental physics contains some astonishing possibilities of which we currently have few inklings. Just possibly we may succeed in scaling up quantum effects to allow ‘ships’ (which will look nothing like rockets) to ‘teleport’ us across space to other star systems but this merely enlarges our non-infinite playing field.

In either case the lifetime of our species will depend directly how unboundedly we exploit our finite resources.

The questions of ‘where’ did the universe come from, or ‘when’ did it begin, now seem like the wrong questions. We have no reason to consider nothingness as somehow more fundamental than something-ness, particularly as we cannot actually observe any nothingness, and we have strong theoretical grounds for dismissing it as unnatural. Nature may abhor a vacuum but it doesn’t permit actual voids, even a vacuum contains structured spacetime. Nothingness ‘exists’ only as an abstraction, like the equally false concept of infinity.

As the universe exists as a ‘natural’ phenomenon then it doesn’t require deities to initiate it, to maintain it, or to eventually destroy it. Nevertheless they do have a more modest reality.

They didn’t make us, we make them.

Humans make gods and goddesses as tools and ‘machines’ to help them. Deities exist as Meme-Machines that have many societal, cultural, and personal functions. They can coerce or inspire not just individuals but entire societies to do or to not do a vast range of things.

Memes, like Genes, evolve by a process of mutation and selection, and basically we apply both the mutations and the selection pressure. Deities that have become ineffectual or whose characteristics have become a survival liability tend to die off, whilst new ones become created from the mutated wreckage of the old, although the devotees of a new or improved deity usually prefer not to acknowledge this.

Our imaginary friends have enormous real effects, so we need to design them carefully.

Newton’s god, so far as we can tell, seems to have had the characteristics of some kind of rational ‘Architect of the Universe’; Newton certainly rejected the messy doctrines of the trinity and the divinity of Christ.

Newton’s vision pretty much encapsulates The Enlightenment’s religious position.

Einstein did not believe in a personal god, but rather he adopted a Pantheistic view of an ordered cosmos, divine in itself. He could never quite accept that the universe behaved with a degree of randomness as the quantum physics which he also initiated, seemed to so strongly imply.

Einstein’s vision pretty well encapsulates the New-Age Humanist’s religious position.

Hypersphere Cosmology, well it suggests that the universe does not require a designer and that its quantum behaviour suggests that it does act with a fair degree of randomness, but in a way that makes it more rather than less divine in itself. A totally causal deterministic universe would have only us, or perhaps not even us, to make it unpredictable. Plus we can make gods and goddesses to our hearts delight and terror.

Chaoism? A work in progress…….

Friday, 23 January 2015 15:41

Thoughts of the Week.

Thoughts of the week.

1) The Transactional Interpretation of Quantum Physics seems to give a more coherent view of Strong Nuclear Interaction than other models. See This may even provide a basis for discriminating between rival interpretations. We mention this because of the very significant metaphysical and magical consequences of quantum transactional mechanisms underlying reality.   

2) It seems particularly bizarre that a secular state such as Britain should fund faith based schools of any kind*. This seems either to arise out of a sense of fairness gone mad, a failure of confidence in its own secular values, or perhaps even a quiet overconfidence that they must eventually always prevail. Faith based schools will always prove socially and culturally divisive. Perhaps the famous British traditions of politeness, compromise, and even-handedness now do it a disservice. Liberalism should not extend to compromises with illiberalism.

*Secularism has become the foundation of British Culture. The ‘established’ Church of England no longer plays any significant role in governance. It now follows rather than leads moral culture.  It remains as a merely decorative appendage to state occasions and as a service provider to a dwindling minority religious interest group. 

A secular, science based, and evidence based culture like Britain should have a religious studies school curriculum which requires familiarity with the overwhelming evidence that all religions without exception have evolved by syncretic processes in which bits and pieces of older religions became cobbled together by humans for various social and political purposes.

This could do more than anything to reduce religion based social decisiveness and home grown terrorism.

Historians and archaeologists should cease to remain the custodians of hard-won and uncomfortable information that we keep away from young people.

3) Leon Brittan dies. The British establishment will however probably wait for a few more of his generation to die before it seriously investigates the allegations. I distinctly remember asking a friend in Reuters about all the accusations in the graffiti sprayed on the walls of London back in the late seventies and early eighties. Everyone in Fleet Street knows, he replied, but it’s unprintable. I also distinctly remember Brittan getting kicked upstairs to the European Comission  by Thatcher after his peculiar sudden resignation as home Secretary.

4) Cameron, ever the brilliant tactician, goes to Scotland bearing insufficient devolutionary gifts, so the SNP will drub Labour and the illiberal dimocrats there in May.

5) The European Central Bank decides, Weimar Republic style, to print a trillion euros but this may not persuade the Greeks from taking the sensible route of leaving the EU. If this initiative fails as seems likely, expect the EU to begin unravelling. Hooray!

See Varoufakis here.

"Currency Union can not prosper due to the lack of any deficit/surplus recycling mechanism." Indeed.

In any nation, capital transfers from richer to poorer regions have to take place to prevent the richer regions from further impoverishing the poorer regions and stimulating rebellion. Basically - if the Germans want Greece they will have to buy it first and then force the Greeks to live and work like Germans. (I assume here that they won't try to invade it again.)

The power-crazed Synarcho-Federalists who put the EU together knew full well that monetary union without political union would not work for long and hoped that the first crisis would end in the political union they sought, however the first crisis turned out rather larger than expected and the appetite for political union within a euro-bureaucracy has diminished markedly.

A european union consisting solely of East Germany and West Germany, with the rest of us doing our own thing now seems like a much better idea. 

6) Lake Chad has apparently shrunk disastrously due to climate change and excessive demands on its waters. Boko Haram appears as a probable consequence.


Thursday, 08 January 2015 10:31

New Years Address.

The 2015 Chaoist New Year Pontifical Address, Stokastimass, January 8th.

From His Pestilence, Pope Pete 1st.

As we languish in the slough of the dog days following the seasonal celebrations and brace ourselves for a coming year of incessant toil, it behoves us to draw comfort from the better events of 2014 and to contemplate the Chaos ahead.

Firstly 2014.

EPOCH, The Esotericon and Portals of Chaos eventually receives a rapturous reception from the esoteric cognoscenti despite a bit of a cock–up at the print works which led to its unavailability for its official launch at the Esoteric Conference at Glastonbury. The memory of standing up at the conference to talk about a book which didn’t actually exist at the time will long remain. Nevertheless soon after we took delivery of them they started to fly out all over the world despite the daunting carriage costs of sending the two kilogram book and card deck package to foreign lands. Matt Kaybryn’s artwork has set an astonishingly high new standard for magical artwork, the concept of extra-large cards for use as altarpiece icons has already proved its worth, and the paradigm challenging text looks set to keep a lot of philosopher-wizards busy for some long time. A party of intrepid volunteers currently seeks to explore the possibilities of the Epoch’s Necronomicon Mythos on Arcanorium College. Hopefully Azathoth of the Nuclear Chaos may have some intuitions to offer on the particle physics front.

Our Eldest finally got awarded her science doctorate, however in the mental aftermath of writing up her brick thick thesis which specially flown in experts from abroad passed without correction, she forgot to book the actual doctoral graduation ceremony, (a bit of a relief all-round actually) so we climbed a suitably symbolic mountain near her highland home and placed a suitably customised mortar board on her head for posterity and photographs.

The Scottish Referendum yielded a thankfully sensible result, one of the world’s most successful political unions remains secure, and the family feud over this matter has now subsided. My arguments and propaganda efforts did not go down well with our eldest who has gone native bigtime with all the fervour of a recent convert, after marrying into a clan up there. You have to admire Cameron’s balls in calling the bluff of the tartan romantics. I hope he does well in the coming May General Election; a Con-Ukip-Green coalition seems like an interesting and agreeable possibility, and an opportunity to distance Britain from the ghastly mess of the European Union. The other two parties seem laughable and without principle or credibility.

Readership of Hypersphere Cosmology on this site suddenly went astronomical and currently stands at nearly three hundred thousand and climbing. The breakthrough in this hypothesis came with the identification and quantification of the mechanism of galactic redshift which arises as a natural consequence of the positive spacetime curvature of this rotating hypersphere of a universe that we call home. So don’t panic, the universe did not arise from a cataclysmic big bang, it doesn’t bizarrely expand at lightspeed, it won’t end in an entropic fade out or a catastrophic collapse and it doesn’t mostly consist of phlogiston like dark matter and dark energy.

This year’s Knights of Chaos campaign scored some notable hits by psychic attack against specific ecocidal projects going on in various parts of the world, but so much remains to do. Nevertheless a consensus grows that in principle humanity must leave the planet’s carbon reserves where they lie, but the practise desperately needs to catch up.

2015.  What Chaos lies ahead?

Particle Physics. Don’t expect any surprises from the Large Hadron Collider when CERN fires it up again. They have probably found all the fundamental particles now and just pouring in more power will only create fleeting composites like the supposed Higgs Boson. The Higgs mechanism remains unproven and unnecessary and in contradiction to General Relativity. Gravity will never reduce to a Gauge Theory. A unified theory will look more like quantum geometry with extra time dimensions, rather than a quantum gravity theory. The LHC may become another Euro-White-Elephant-Mega-Financial-Disaster-Investment if desktop Wakefield Generators come online this year and do much the same job. (I may get one myself.)

Cosmology. Expect to read a lot of sense in the forthcoming book: ‘The Singular Universe and the Reality of Time: A Proposal in Natural Philosophy’. Hardcover – 31 Jan 2015 by Roberto Mangabeira Unger and Lee Smolin

The publication has become a little delayed but from pre-publication reviews and e-book reviews it would seem that these two gentlemen, the first a Philosopher and the second a Physicist, call for a reversion to the principles of Natural Philosophy when it comes to cosmology and the big questions about existence because the current cosmological ‘physics’ has let the mathematics run away with itself into realms of crazy speculations about singularities, dark matter and dark energy, cosmic inflation, multiple universes, multiverses of multiple universes, or a block universe where absolute causality reigns supreme and time has no real meaning, with each of these otherwise unsupported conjectures acting as articles of faith for various cliques of believers in the unreasonable effectiveness of mathematics even in the absence of any sort of observational confirmation.

It may well prove a seminal book.

Earth. The plague of humans on this planet shows few signs of self-control when it comes to population growth or resource consumption. We burnt 43 gigatonnes of fossil fuels last year and we seem set to exceed that this year. Expect unpredictable extremes of weather. Whether the human population of this planet by the end of this century will reach 10+ billions or whether it will collapse back to a few hundred thousand hunter-gatherer-scavengers remains an open question.

A world human population of 500 million and an environmentally neutral steady state economy seems the only sustainable long term policy. The challenge remains to achieve this without passing through a phase of civilisation wrecking catastrophe first.

Many of the Islamic countries seem caught in a very difficult position; the theological differences serve only as convenient flags for the underlying problem of conflicts of population and resources. Nearly all of those countries have huge and still growing populations living on rapidly diminishing resources, and cultural attitudes which often inhibit the social and technological reforms which could ameliorate such problems. In the meantime expect the situations to worsen indefinitely.

Beware of any meme complex that cannot tolerate criticism, humour, apostasy, or blasphemy. It means that its own internal contradictions will make it behave violently.

Moral Philosophy. Don’t expect any major changes of moral fashion in 2015. Those who have had their sexualities legalised will continue to opine upon the involuntary nature of such orientations, whilst society will continue to opine upon the elective and punishable nature of illegal orientations. Law and Disgust continue their cultural dance. Necrophilia with prior consent will probably still remain illogically illegal. The victimless crime of sex with other animals will probably continue to attract surprisingly harsh punishment despite that the killing and eating of other animals remains approved. Violence, murder, and war will provide much of the entertainment for all ages as usual, although the slightest hint of sex will still trigger an avalanche of restrictions. Offending fat people may become politically incorrect and then illegal if the fat lobby can prove itself involuntarily fat. Sick old humans will remain condemned to suffer for as long as possible whilst we will continue to put down sick animals at the slightest sign of distress (to us). Sometime in 2015 expect the emergence of a euphemism for ‘unacceptable’, a word which has become tiresomely over used to imply that everyone should dislike what the speaker dislikes. Also the current official PC euphemism for ‘Dimwit’ may become due for its five year replacement.

Magic and Esoterics. The excitement of the last magical revival which began in the late 1960’s shows definite signs of cooling with fewer young magicians taking up the wand at present, the hardcore survivors getting older, and fewer innovative titles becoming published. Basically the 1960’s revival began as a resurgence of a paradigm rooted in Platonism and Neoplatonism and coloured with Neo-Paganism and Orientalism, against the growing current of scientism and the decline of religion in western culture. It took many of its cues from the previous magical revival in the 1880’s when the Romantics tried something similar in the face of growing Industrialism.

The recent revival has left two legacies, firstly it has kept alive the third way of thinking, the magical one, as opposed to the scientific and the religious ones, and this continues as a sort of softcore new-agey factor in many peoples thinking. Secondly, as the revival developed, some theorists began to question the underlying Platonist and Neo-Platonist metaphysics which supported both conventional religious and conventional magical thinking to a considerable extent, and speculated on whether they could replace it with metaphysics based on quantum physics instead.

The mind-body dualism has become as suspect as the spirit-matter dualism and the Platonic essence-substance dualism, whilst the wave-particle dualism has become physically demonstrable, if only in limited circumstances, and it promises a mechanism that could nowadays more comfortably provide an explanatory model for magic. In religious aeons magic tended to share its metaphysics with religion, today it moves towards sharing its metaphysics with science.

The removal of the Platonist essence-substance model form magic would weaken the hold of the spirit-matter model of most contemporary religions. This pernicious idea underlies most of the justifications that religions use for their appalling behaviour on the material plane.    

However this paradigm shift remains a struggle in progress, the old model falls into disrepute but the new one remains somewhat obscured by confusion, ill-informed enthusiasm, and the intellectual difficulties associated with any non-trivial new concept. Expect another magical revival as the new paradigm achieves greater coherence, its own vocabulary, and a more widespread understanding.

Over the last year we have found much of interest in the breathtaking scholarship and the musings of the grumpy old Archdruid of America, John Michael Greer: -

However his other blog on the decline of technological civilisation: -

Provides a sobering and sometimes terrifying read.

We live in interesting times, welcome to 2015. Pete. 

Thursday, 18 December 2014 20:44


An interest in Druidry has led me to an exploration of the 'Spirits of Place' of this area. The local Celts had a Goddess of the Cotswolds that they called Cuda. Cotswold probably means Cuda's-wold. Stone engravings of her still exist at Cirencester, the old capital of the Dobunni tribe hereabouts.

She appears as a goddess of prosperity and sits enthroned holding something suggestive of a baby or a loaf or an egg, and surrounded by three mysterious figures, the Genii Cullculati.

This area has remained prosperous for thousands of years. When the Romans arrived the Dobunni cooperated with them and the area became of of the most desirable 'suburbs' of the Roman empire.


Today it remains one of the few areas outside of London where the economy remains upbeat. I hitchiked to this city of Bristol perched on the edge of the Cotswolds some thirty years ago with just my girlfriend, a sleeping bag, two hundred quid, and the prosmise of a friends sofa. It has proved bountifull for us beyond measure, and making this statue became an act of homage and thanksgiving for the prosperity and natural beauty of the area.

As we discussed the form She would like to appear in today we settled on a ramshorn hairstyle as a nod to the sheep-rearing that has gone on in these hills for millenia, the egg represents bounty both material and spiritual. The Genii can represent elves, Druids, landwhights, or maybe the hills themselves.

I couldn't resist giving the Genii candles in view of the season, I will take her to the midwinter solstice of the Grove on Sunday.

A Merry Solstice, Mithrasmass, Saturnalia, Christmas, or whatever you celebrate, to all my friends and colleagues and readers. Pete.

PS, see:


At least some respectable physicists entertain hypotheses of hyperspheres and three dimensional time.



Monday, 08 December 2014 14:22


 The symbol shown here represents a Hypersphere, sometimes called a three-sphere, or a 4-ball, or an S3 manifold.In such a hypersphere the internal 'diameter' or Antipode length equals half the circumference, making it somewhat 'larger on the inside than on the outside'. Its resemblance to the Taoist yin-yang symbol seems most pleasing, the classical oriental mystics thought of most things at one time or another although not always in simple to understand terms.  

The Hypersphere Cosmology section of this site now contains several new papers dealing with aspects of the main hypothesis in more mathematical detail and with more detail on the physical principles implied. 

Hypershpere Redshift shows the mechanism by which the small positive curvature of the non-expanding universe redshifts light from distant galaxies. 

Hypersphere Rotation shows the derivation of the equation for the four-rotation of any hypersphere derived from Godels three-rotation of a simple sphere. Any valid derivation from an exact solution of the field equations of General Relativity presumably has its own exact solution in there somewhere.

Hypersphere Holometry derives from the Beckenstein-Hawking conjecture about the relationship between the information content of a black hole and its surface area. If true, and if applicable to hyperspheres, the conjecture leads to a prediction about the quantisation of space and time which Holometry experiments in progress may validate.

Hypersphere Visualisation and Lensing shows a fairly simple method of visualising what a hypersphere 'looks' like, and the lensing diagrams show how a hypersphere will distort sight lines across the universe creating the optical illusion of an apparent acellerating expansion.

On an entirely different matter Pactionis 2, first presented on a blog here in 2013, reappears in the Wizardry section, because it needs to. 

Wednesday, 26 November 2014 11:06

Hypersphere Cosmology

Hypersphere Cosmology

An exhausting 30 day battle has just finished on the Cosmo Quest Physics Forum:

(See ‘Against the Mainstream’ section.)

This battle, fought mainly with n-dimensional algebra through many a sleepless night, ended with the massed advocates of standard cosmology at a standstill and throwing in the towel by invoking a 30 day rule to avoid a retreat.

During the conflict, worldwide mass googling of ‘hypersphere cosmology’ brought the following obscure scientific paper, published in June 2014, out of the woodwork and up the rankings:

‘On the Physics inside a Closed, Static, Rotating Einsteinian Hypersphere in Due Consideration of the Galaxy.’

Beneath the blizzard of algebra and differing notations in this paper, it seems obvious that its theory exhibits almost complete isomorphism with hypersphere cosmology as presented on this site, and previously published in outline form in a natural philosophy treatise - The Octavo 2011.

It would seem that the Natural Philosophy approach and the Hard Science approach have come to identical conclusions here.

Natural Philosophy theory tends to start with physical principles derived from reason and imagination and then tries to wrap some maths around them to check their validity. Hard Science theory tends to start from accepted physical principles and then tries to extend them by mathematics. 

Because we can think of far more physical principles and far more mathematics than the universe actually uses, both endeavours can run into problems. Both approaches require the reality checks of plausibility and experiment.

The hypersphere cosmology hypothesis began with the natural philosophical intuition that the physical principles implied by the initial conditions of the big bang theory remain totally implausible.

We can only rely on ‘The Unreasonable Effectiveness of Mathematics’ when they don’t lead to implausible solutions that require dozens of equally implausible patches to shore them up, like singularity theory, cosmic inflation, dark energy, and dark matter.

We may now confidently expect the replacement of all variants of the big-bang-expanding universe theory with variants of hypersphere cosmology theory within a few years.

This may upset a number of older physicists but it will provide plenty of work and excitement for the coming generation of bright young physicists.

It may also upset the Pope a bit, which seems a pity because the current one seems a nice humanist type, but nobody has infallibility, and maybe the idea of a deity who doesn’t start the universe with a cataclysmic explosion and who doesn’t end it all with a feeble entropic fade out or a crushing collapse, may catch on.    

Monday, 03 November 2014 21:36


Herewith Lugh, one of a series of Celtic Gods associated with my area as the pan-celtic god Lugus and his welsh counterpart Lleu.  

In the recorded Irish myths he appears as the thinking man's superhero - a wright, a smith, a champion, swordsman, a harpist, a hero, a poet and historian, a craftsman and a sorcerer. 

Anything you can do Lugh can do better - as the Prof has quipped.

In this faux first century bronze (rendered in metal and milliput) I've depicted him with a mercurial style magic spear (the Romans equated him with their Mercury) and a slingshot at his belt and a harp for his atributes in the Irish myths. 

Wednesday, 15 October 2014 18:27

Academic Paper

As no tenured academic seems to want to risk career suicide by endorsing the following scientific paper for journal publication I release it here into the public domain for free use.

It's located on the Hypersphere Cosmology section of this site.

Unfortunately its radical conclusions may invalidate the current work of some 20,000 or so theorists, however it will give them plenty to do with the rest of their time.

Perhaps doubly unfortunately this all comes from an old style Natural Philosopher and Wizard, but don't let that inhibit your rigorous investigation of the maths and physical principles that it implies.

And on a lighter note see my impression of Sulis, Goddess of the hot springs at Bath, 1st century romano-celtic bronze in the neo-barbaric style :) actually rendered in milliput and steel wire framed, black lacquered and verdigrissed, I hope they like it at Grove. Impression of Lugh to follow.

Friday, 19 September 2014 16:42

Autumn Equinox


Autumn Equinox and my three Mandrakes have again sprouted leaves after a dormant summer; I guess I must have the Autumnalis variety. They certainly take their time; I may just get some flowers and seeds this year. Milady, the largest one who looks like she reclines cross-legged on a couch, has achieved the size of a modest parsnip in 3 years. My cunning plan to re-seed all the hedgerows of southwest Albion with the m may take centuries.

Walking over the peaks in the north of the Lake District earlier in the week I could see Scotland and wondered if I would ever see it again.

But Scotland just said YES to common sense, despite the juvenile element to the vote. The canny Scots will get devolution and even more of our money and they will retain British citizenship, and I won’t have to send food parcels to my eldest in the highlands.

Cameron will probably get re-elected now, and hopefully buoyed by his success he will grant us all a referendum on the EU……. and loose it.

Divorcing Britain to get closer into bed with the damned EU always looked like the Achilles heel of the argument for Scottish Independence.

The Wizardry section of this site now contains a new piece called The Neoplatonic Chocolate Screwdriver. Ever since I picked up my first books on magic and esoterics forty years ago I’ve had issues with certain dubious parts of the corpus like astrology and the essences of the elements. My experiences of Neo-Druidry have served to crystallise my thoughts on the subject further, I love the overall ambience of Druidry but the Neoplatonism in it leaves me cold. 

Wednesday, 10 September 2014 14:11


Scotland, bonnie Scotland, adopted home of my firstborn. Please take the new Devo Max option and vote No to the foolish romantic notion of a hasty divorce in favour of that damned European Union. Stay and we can go Independent together.

If the hotheads of the Yes campaign loose expect a few brawls and some vandalism, but if they win expect massive disinvestment and refugees migrating south.


In other news: -

Hypersphere Cosmologyachieves 150 thousand+ hits from all over the planet!

Do keep me informed of your debates with the timid tenured guardians of cosmological orthodoxy, I hope to outlive the big bang theory.

Epic Fail. IOT Pastgrandmagus Fails First Grade of Druidry!

Oops, well at least it’s useful to know just how high they set the bar these days.

I shall nevertheless remain a Bard and continue at Grove, and with my studies, differences of opinion over Neoplatonist metaphysics notwithstanding.

Insanesburys. Sandwich and a juice? That’s £4.19 Sir, mind you, if you have a packet of crisps with it, it will only cost you £3. Okay thanks mate, ring in a notional packet of crisps as well then. Sorry Sir, but you will actually have to take the crisps as well; shall I get them for you? Err thanks, do you fancy them yourself. Sorry Sir but I’m not allowed to accept them. No wonder we have an obesity crisis, even amongst the pigeons in the park.

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