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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.

Sunday, 10 August 2014 20:34

Natural Philosophy

Natural Philosophy.

On Saturday night I attended with friends the open-air Robert Plant concert at Glastonbury Abbey. This event seemed a thousand miles away from the big annual Glastonbury pop festival, no mud, few twentysomethings, mainly nine thousand senior folk with their own portable chairs, picnic tables, hampers and champers, and sometimes their kids.

The Maestro gave a spellbinding performance, the elder god of rock looks like Odin now but he still sings like Apollo. He covered a number of old Led Zeppelin songs but gave them all an upgrade with fresh twists and subtleties and some new ethnic inputs from his band which included a very talented guy from the Cameroons. By the end of it he had all of us oldies up out of our portable chairs.  A master of his craft finessing his career.

I note that the Hypersphere Cosmology in a Nutshell paper here has already notched up eighty thousand reads. A new more powerful equation has replaced the redshift equation given in The Octavo. Either the world’s physicists must have started passing the joke around to all their mates or they have started scribbling furiously on their blackboards.

I suspect that the flurry of interest may have arisen because of the ‘axis of evil’ that the WMAP probe recently revealed as an embarrassing anisotropy in the cosmic microwave background radiation could bear interpretation as some sort of rotation of the entire universe.

To forestall the possible headline ‘Mad Occultist Cracks Secret of Universe’ I’m redefining myself as a Natural Philosopher. Natural Philosophy was what we used to have before science and magic parted company after Newton. Somewhat paradoxically Newton himself researched alchemy and esoterics and science and maths with equal vigour, but we only tend to remember the old sorcerer-scientist for his science and maths. Me, I like to look at the bigger picture too.

So I’ve decided to try and pass the Bardic Review and apply to become an Ovate.

Monday, 28 July 2014 15:04


Welcome to the upgraded Specularium website, Anti-Social Media at its best, you cannot post replies here but you can email and initiate a discussion of serious ideas.

Those wishing to initiate serious discussions about esoterics and science, art, magic, politics, and religion in general may care to participate in Arcanorium College. Debate here proceeds according to the highest standards of civility and intellectual discourse, to maintain this we levy a minor subscription which frees us from spam, incivility, and nutters, yet we do allow a probationary free membership for a couple of weeks.

I haven’t the time for internet social media. I prefer the more measured and thoughtful interaction that Arcanorium College offers.


This Specularium site has 3 major sections and a blog. Many have wondered why a wizard chooses to devote so much effort to scientific speculations, a recent item in a debate on the Blog of Baphomet clarifies this issue: -

‘Wizards of old had to have a detailed working knowledge of religion, for religion formed the cultural and intellectual backdrop to their times and they would have fallen foul of it, or appeared stupid, without such knowledge. Today’s wizards need to familiarise themselves with science for exactly the same reasons.’

Plus any sort of esoteric or magical hypothesis implies some sort of Rebel Physics, some sort of extra component to reality that requires explication or refutation, and which may lead to a more comprehensive understanding of the profoundly peculiar reality in which we find ourselves incarnate. When you look at the sharp end of physics in the quantum and cosmological domains the standard conventional models look full of holes and contradictions and unresolved questions, leaving many metaphysical assumptions open to potentially fascinating debate. The Path of Knowledge needs to encompass all that we can know, including the contra-intuitive and the peculiar and the esoteric. Much of what now passes for science previously lay in the domain of wizard’s speculations. Let the titanic struggle continue!

Anyway, on a more mundane note, a few observations about Book Zero.

My contacts inform me that Ray Sherwin recently sold a handwritten manuscript of Psychonaut to an unnamed American collector for an undisclosed sum. Plus Ray, with whom I exchange approximately biennial emails, informs me that he has recently retired to the sun with a nice little villa in Fuerteventura.

Methinks these events may have a connection, if so, well done Ray, enjoy the proceeds. The manuscript in question had long ago faded from my attention. The natural products business idea I borrowed from you has made me millions, even though you in your inimitably laid back style didn’t go all the way with it yourself.

I do however wonder exactly which manuscript this concerns. Before departing for a couple of years in India and Australia I left a first Liber Null manuscript with the Morton wizard and eventually received a single copy of Liber Null with a White Cover whilst in Australia. This proved invaluable in setting up the Church of Chaos down under for the duration of my stay, the eight of us did tremendous work in the basement of the self-styled Lord Vegtam’s apartments. Ian Johnstone, do you still live?

On the way back I rewrote Liber Null in the foothills of the Himalayas and this manuscript became the basis of the Red Cover version of Liber Null which Ray and I made about 400 copies of and sold mainly to The Sorcerer’s Apprentice in Leeds during my 2 years in Yorkshire at Ray’s village in East Morton. We collated and glued the books together in Ray’s kitchen. This red version became the text adopted by Weisers and eventually rolled into a single book along with Psychonaut which I wrote on my return to the UK. I had thought that I'd given the Psychonaut manuscript to The Sorcerer's Apprentice for their initial Brown Covered A4 edition.


Ray always seemed vague and evasive about just how many White Cover Liber Null’s he made. The one I had eventually got lost or given away sometime after I moved to Bristol. I never saw another, rumour has it that only either 2 or 5 got made.  So this little tome, whimsically titled Book Zero, that sunk a hundred paradigms and launched a hundred more, actually came out in a sort of ‘zero’ edition limited to perhaps 2 or 5 copies. Does anyone know what became of them? 

Anyway in the longer term, having recently acquired sachet making machinery, in a few decades my executors will market my ashes, attractively packaged in 10g sachets, partly for the pleasure of esotericists of an essentialist persuasion, partly for use in occult art and science, and partly to offset the rapacious death duties on my estate. Prices on application, (probably in Chinese Yuan/Renminbi) when the time comes.

Supplemental : A correspondent just sent me a pic of a White Cover Liber Null. It bears the number 50 of 100 and contains what looks like a brief message from the author and a signatorial squiggle, neither from me methinks. What did the mouse do when the cat went off to the Himalayas?

Monday, 02 June 2014 13:59


Eurosceptic parties of the left and of the right have made a good showing at the elections for the sham ‘EU Parliament’, and UKIP have done exceptionally well in the UK. The response from the unelected EU commission and the Germans appears to consist of: - ‘we will make a pretence of listening to the protest but we will basically ignore it and hope that it will go away when the economy improves’. The ‘ever closer union’ faction of the euro political class remains in power but the tide has started to turn.

The EU economy seems unlikely to ever improve now because energy and raw materials become ever more scarce and expensive, and dynamic emerging economies with cheap labour look set to dominate future markets. An over regulated synarchist managed, undemocratic and creatively inhibited europe hamstrung by political correctness and gigantic social security bills seems set for decline. The EU will reap a hurricane of revolt next time if it continues to ignore calls for a complete rethink of its function or for its dissolution. UKIP has done the British a huge favour by providing a Eurosceptic alternative to the BNP, the French eurosceptics had little alternative but to vote for the National Front.

UKIP’s triumph seems a fitting kick in the teeth for the Guardian reading classes and the illiberal dimocrats. The party of little more than ‘neither of the above’ has become trounced by a party with serious alternatives. (It just seems a pity to me that UKIP’s environmental policies seem very poorly scientifically informed.)

The widespread attempt to accuse UKIP of racism has backfired spectacularly. Whilst the party (like any other) probably does include some individuals with such opinions, its general stance appears Culturalist rather than racist. Most Brits don’t feel too bothered about skin colour but they do object to militant multiculturalism and believe that some cultures have stupid and ineffectual ideas and inhumane value systems.

Since the sixteenth century the foreign policy of the British has centred upon denying anyone hegemony in Europe. Thus they fought the Spanish, the French, and the Germans for centuries and then opposed the Russians throughout the cold war simply to prevent anyone dominating continental Europe. The strength of Europe lies in its diversity and the ability of its various separate nations to try experiments with different approaches. Britain reinvented democracy and taught it to the world, now it must struggle again to prevent Europe descending into an undemocratic Soviet or modern Chinese style hegemony led by an unelected and unaccountable synarchy of the  political classes hiding behind a vast faceless bureaucracy.

I do hope the Scots see sense before their independence referendum. If they want more independence then trying to throw their lot in with the EU will have exactly the opposite effect. They would do better to negotiate more independence for themselves within a UK free of the EU. Tartan romanticism would eventually become heavily regulated by the EU you know, expect 5,000 pages on the health and safety and political correctness of kilts and sporrans and bagpipes, and you can forget about those sock dirks.

The Epoch seems to have received rapturous reviews from everyone who has read it


The basic Platonic-Pagan-Monotheist paradigm which has dominated esoterics since the first centuries of the first millennium until quite recent times has finally met its fully formed nemesis and replacement in the Quantum-Neo-Pagan paradigm. The new map of esoteric reality looks disturbing and challenging………. and strangely beautiful.


Page 8 of 15
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