Arcanorium CollegeCollege News and Views

Pete Carroll

Tuesday, 16 February 2016 19:47

Asymmetric Combat Polygons

Asymmetric Conflict Polygons

Uncertainty in games can come from either building in randomness with dice or shuffled cards or some other sortilege procedure; or from scenarios where players lack information about their opponent’s intentions.

Simultaneous Play often yields a system that models real life scenarios rather well. In this, the players secretly record their intended plays and then all reveal their orders and compare them to see what happens. The game of ‘Diplomacy’ which simulates the political alliances and military balances in Europe from 1900 onwards provides a classic example of a game based on simultaneous play with concealed intentions. Only rarely does peace prevail until 1914.

Some people find the use of dice or some other random mechanism unappealing as it can make the best laid plans come to nothing for no reason except bad luck, and it prevents any detailed analysis of a game afterwards.

The game of Scissors-Paper-Stone, sometimes called ‘Roshambo’, may well originate from the Han Dynasty era in China. It has attracted a considerable amount of study and competitive play, and computer algorithms exist against which humans can play. Although no strategy can consistently beat purely random play, competitions and algorithms remain interesting because few people can consistently play randomly and a good player or algorithm can anticipate the non-random choices of an opponent based on their previous choices.

Nevertheless the game remains rather trivial although the principle has become incorporated into some games to settle combats between pieces, for example in hand to hand conflict, Parry and Thrust beats Lunge, Lunge beats Slash, and Slash beats Parry and Thrust, or something like that. To a very simple approximation circa 1805, Artillery beats Infantry, Infantry beats Cavalry, and Cavalry beats Artillery.

Such a system of conflict resolution leads to a quick and easy type of duelling done with hand gestures, or with cards selected and put forward and then exposed. Yet in its simple form it seems little better than using dice. However by using something a little more sophisticated than a simple symmetrical triangle of outcomes we can create a facility for meaningful tactical choices with some uncertainty of outcome.

Consider the virtues of Asymmetric Conflict Polygons. An Hexagonal one appears below.

In this the six choices can represent any tactic from the exchange of fire between starships to the exchange of spells in a magical duel. The arrows between tactical choices show which choice wins and the weight of the arrow can show by how much. Each player in the duel has six cards marked with the tactical choices and both draw a card and then they simultaneously expose them and find the result. The asymmetries in the chart make some choices more favourable than others, depending on the powers of the pieces involved, however obviously the opponent will appreciate this.

The actual chart shown has the design feature that no choice offers guaranteed immunity from a full hit, but some choices offer greater chances of some kinds of hits.   


We could display the information on such a polygon with a simple 6 x 6 chart, however the polygon itself gives a much easier to use representation of the effect of one tactical choice upon another and the opportunities for second guessing the opponent.

Conflict polygons can also model the effects of offensive against defensive tactics where the attacker draws an attack tactic card and the defender draws a defensive tactic card.

In solo play an asymmetric polygon can allow the player to compete with intelligent choices against random choices generated by dice rolls. 

Tuesday, 16 February 2016 19:36

Napoleonic Chess

After decades of creating games of sometimes almost unplayable complexity the following game of Napoleonic Chess just sort of fell into place as part of a dice-free battle resolution system within a much larger strategic geo-political and economic game scenario. (I still work on that, particularly the naval aspects.)

 However the game of Napoleonic Chess ™ has such an elegant simplicity and playability to it that I declare it Copyright Peter J Carroll 16/2/2016 ©.

Napoleonic  Chess.

A tactical game system for Napoleonic era battle simulation which players can use on an ordinary chess board using chess pieces, or extend to larger boards, add terrain features, or add additional units. This system differs radically from chess in that players may move all of their pieces in their turn.

The basic rules for the Standard Scenario appear below, followed by suggestions for more sophisticated scenarios.

Standard Scenario.

Players set up as shown with units on the 2nd and 3rd and the 6th and 7th rows. If using a standard chess set, discard the queens; use the pawns as infantry, knights and bishops as cavalry, rooks as artillery, and the king as guards. Alternatively for a better appearance and ease of use, take 2 chess sets and use all the knights for cavalry and both queens for artillery on each side. Alternatively acquire or make some period pieces.

Each side moves alternately and settles all resulting attacks, and each player may move all their units during a single turn.

Movement and Combat. Units basically move (or not) and then attack in a single turn.

Infantry may move a single square in any direction.

Infantry attacks or supports orthogonally only, with a value of 1, into an adjacent square. Infantry has a defensive value of 1.


Cavalry may move one or two squares in any direction.

Cavalry attacks or supports diagonally only, with a value of 1, into an adjacent square. Cavalry has a defensive value of 1.


Artillery may move a single square orthogonally only.

Artillery attacks orthogonally only with a value of 2, into an adjacent square.

Artillery supports into an adjacent orthogonal square with a value of 1.

Artillery has a defensive value of 1.


The Guards may move a single square in any direction.

Guards attack or support in any direction with a value of 1, into an adjacent square.

Guards have a defensive value of 2.


Any unit may make only a single attack or defensive support in a players turn, or a single defensive support against attack in an opponents turn.


Eliminating pieces.


Any unit coming under attack by attack values which exceed its defence value plus the value of any support it receives becomes eliminated and removed from the board.


One of the attacking units may then move straight on to the square it occupied if the attacker so wishes.


A unit under attack cannot offer support to an adjacent unit.


Victory Conditions. Elimination of the enemy Guard unit; or the enemy surrenders.

Example of a complex attack.


Here Red attacks the Black Artillery unit with Artillery. The 3 orthogonal Black infantry units support the Black Artillery but the support of the ones on either side becomes removed by attacks from Red Infantry and Red Cavalry, so it only has support from the Black Infantry behind so it has a total defence value of 2, whereas Red attacks it with an attack value of 3, one from the Red Cavalry and two from the Red Artillery, so it becomes eliminated. Red then has the option of immediately moving either the attacking Red Cavalry unit or the Red Artillery into the vacated space. (Although this would prove very risky).

Advanced Scenarios. 

1) Alternative Standard Scenario Initial Dispositions.

a) Attack at Dawn. Both sides write down their desired positions of their units on the 2nd and 3rd and the 6th and 7th rows in secret and then reveal them and lay out their units.

b) Marching Orders. Players take it in turn to place one unit (or more if agreed) on the board at a time in the appropriate rows till all units have become deployed.

2) Additional/Variant Units.

Horse Artillery moves 2 squares in any direction.

Horse Artillery attacks and supports in any direction into adjacent squares with a value of 1.

Horse Artillery has a defensive value of 1.


Dragoons move two squares in any direction.

Dragoons attack and support into orthogonal squares only with a value of 1.

Dragoons have a defensive value of 1.


Foot Guards, as for Infantry but with a defensive value of 2.


Cuirassiers/Horse Guards, as for cavalry but with an attack value of 2.


3) Optional Terrain Features. (Made by placing an appropriate card tile on a square)


Hills – add one to the defensive value of a unit on a Hill square unless attacked from an adjacent hill square. Units cannot move on and off a Hill in a single turn.


Redoubts - (earthworks etc.) - these take an agreed number of turns of uninterrupted occupation of a square to construct, and then function as for Hills. Artillery attacking into a redoubt attacks at only 1, and cannot enter an enemy redoubt on the same turn if it falls.


Square Border Obstacles – watercourses, banks, ditches hedges etc. – These can mark one or more of the edges of a square. They give +1 defensive value if they protect a unit from all units attacking it. Artillery has only an attack value of 1 across such obstacles.


4) Larger Boards, Bigger Battles with More Units, Multiple Armies, Multiplayer, Divided Command and Strategic Scenarios.


This system will support all of the above. Allied units from different armies or command structures may support each other by attacks without moving, or by supporting in defence.


In Strategic Scenarios stretching over continents and using markers for entire armies, this system provides a means of resolving battles at a tactical level.

In larger battles it often helps to number the pieces to keep track of which have moved and which haven’t in a turn. 1st, 2nd and 3rd infantry etc.

 Other Epochs. This battle system can support a variety of pre-gunpowder conflict scenarios by simply substituting Heavy Infantry for Artillery.

Monday, 15 February 2016 20:21


February Blog.

The POTUS campaign. (President Of The United States)

The popularity of the presidential candidates Trump and Sanders seems like the inevitable symptom of the relative decline of America. Since American industry and the American military have ceased to dominate the planet, America’s real economic growth has stalled, but America’s professional class has continued to take more at the expense of America’s waged class.

Thus the American political consensus has started to unravel and voters begin to entertain far from mainstream candidates.

Trump and Sanders each have a different approach to this problem from opposite ends of the political spectrum.  However in the first case regaining industrial and military supremacy seems unfeasible, and in the second case socialism would come at the price of huge social upheaval against vested interests.

Militarism will no longer work in the context of a world awash with cheap geo-politically defensive weaponry and asymmetric warfare, unless you want to make liberal use of WMDs.

Socialism does not seem compatible with the present demand-economy structure.

America needs to look to the health of its manufacturing base and to apportion its wealth accordingly. It also probably needs to adjust to a lower growth model across the board.

The EU Referendum.

David Cameron seems like a brilliant tactician and he seems unlikely to lose the forthcoming EU Referendum, but will he have to change sides to win it? He would probably like to remain part of a completely redesigned European organisation but he knows that he won’t get that.

Problematically for Dave he has to make a show of renegotiating the UK membership to assuage those members of his own party who stand to benefit from the EU’s favouritism towards the interests of big business (against small business) and the political class (against the people).

The reform proposals on the table look cosmetic and paltry and will rapidly become completely ridden over if we capitulate and agree to stay in.

Fear of the unknown may induce some to want to remain in, so the out campaign should focus heavily on visions for an Independent Britain.

The greatest unknown however surrounds what will happen if we decide to remain in. What new nonsensical burdens will the EU impose? What further loss of control of our own affairs shall we suffer? Those of us old enough to remember the first referendum on the Common Market now seem at the forefront of the out campaign – we saw how voting for one thing brought quite another.

If Britain leaves the EU now we could bring down the whole rotten structure, liberate the nations of Europe and restore democracy.

The EU Synarchy remains well aware of this and thus it has a massive incentive to lie, as indeed it did about the ultimate agenda of the Common Market.

As a sort of metaphor for the EU consider the virtues of ABOLISHING BELGIUM.

‘Belgium’ functions as the ultimate adjective of vilest abuse in almost all the languages of the cosmos according to Douglas Adam’s Hitchhikers Guide to the Galaxy, and deservedly so when you consider the history and the current state of the place.

Belgium has always functioned as a sort of awkward weak buffer zone between the west and east Franks (roughly the French and Germanic language groups). Its existence has facilitated most of the bloodiest wars of history. Most Belgians don’t even want Belgium to exist; half would prefer to join the Netherlands and the other half would like to join France. Nobody can recall any famous Belgians because any who become famous usually prefer to imply that they came from somewhere else.

As a sort of unloved ‘in-between place’ with no coherent identity of its own, Belgium suffers from a brief but appalling colonial history, chronic maladministration, and far too many unassimilated immigrants from other cultures. It has become a haven for crime and corruption and the dodgy arms trade, despite its viciously heavy handed policing at low levels. (Don’t go on holiday there unless you intend to behave very obediently and quietly.). Its national monument seems to consist of a boy urinating into a fountain. No wonder the Synarchists behind the EU decided to use Brussels as a facade for their activities, this rotten heart of Europe provides the anonymity from which they and their German paymasters can piss all over the rest of us.

The EU, I loathe it, it looks totally BEL***M!

Because they modelled it on that damn place!

Anyway, despite the trials of February in the northern hemisphere (Peak Suicide and Peak Misery Month, worsened by Lousy Weather, and for many, also by Valentine’s Day, plus we attempt a Saturn working on Arcanorium College.) I do have some uplift for you: -

Welcome to the Specularium Game Theory pages, see the site header bar.

Materiel on Napoleonic 'Chess', Assymetric Combat Polygons, The Astronomicon, and more, to follow.

I’ve had a fascination with games, particularly board games, since my earliest times and have played hundreds and designed dozens more of them. We all have mental models of our universes inside our heads. Sometimes the effort of actually laying the geography out and formally abstracting the rules and the uncertainties pays unexpected dividends.

Thursday, 21 January 2016 11:43


I have become a grandfather for the first time, with my eldest daughter and her husband creating a delightful daughter a couple of weeks ago, mother, baby, and husband all doing fine. As my eldest has become an SNP convert in her adopted homeland, my granddaughter bears a suitably grand Scots-Norse name.

This sort of immortality plus a modicum of literary immortality will do nicely; no other form of immortality actually seems desirable if you think carefully about it.

And now to technical advances in esoterics: The picture shows the new Epoch Planetary Pocket Wand, currently loaded with the Horus Lamen, plus the other Martial Lamens for Athena, Choronzon, Thor, Mars, Eris, Loki, and Ishtar arraigned around it as we conduct a series of invigorating Martial workings for January in Arcanorium College. The whole set of Planetary and Bi-planetary Lamens consist of plywood carpentry biscuits pointed up and painted and ensigilised. The Lamens serve both as wand loads and as movable symbols for use on an Astronomicon board.

Wizards often tend to fashion and to discard wands, both Longstaffs and pocket sized Purbas, throughout their careers, both to assist practice and to mark the development of their ideas. This one probably qualifies as about my Mk 11 Purba, although in some sense it also qualifies as Marques 11 – 47 all in one go, due to its versatility. Carrying a pocket wand began as an exercise in Chaos Monasticism, but it has become a constant practise, reminding the wizard that the calling, the duty, and the opportunity, remain ever present.  

The festive and birthday period brought this remarkable book: -

Most religions have something running from unease to downright rejection towards the Theory of Evolution, but perhaps much more than the simple inconsistencies between scriptural depictions and scientific ideas about the origin of species underlies this. 

The book traces the origins and survival of many of the religious and mystical ideas from India through the Middle East to Europe. As most serious scholars have understood for decades now, religions get cobbled together from the memes of previous religions, they don’t spring miraculously into existence out of nothing, and having cobbled themselves together from fragments they continue to evolve and develop, whilst pretending that they haven’t.

Zoroastrianism, the religion of the Persian Empire, went into decline, although it still has a tiny following.  However Judaism seems to have adopted some Zoroastrian ideas fairly early on in its development and these later fed into Christianity. The Pythagorean philosophies from classical times continue to influence some minority sects in the Middle East. Mithraism has left at least one very distinctive and surprising mark on European culture. (I won’t spoil it for you, read the book.)

Emotive Religion. Theology looks like the attempt to psychoanalyse Deities from the characteristics they display in scripture and in lore and perhaps in ‘revelation’. We try to second guess or interpret their supposed wishes by such activity, usually to some sort of advantage to ourselves.

Mythology and the History of Religion tend to tell us more about how our human psychology expresses itself in various situations than about the Deities themselves.

Theurgy describes the attempts of magicians to call, conjure, and even coerce, various spirits and deities, on the assumption that such phenomena have some sort of independent metaphysical reality. It seems like an extreme extension of prayer.

Theometry on the other hand implies taking the measure of Deities, including noting how our projections of them has evolved, and also making them to order, on the assumption that such phenomena arise from our own psychology and may also serve as vehicles for liberating our more unusual abilities. This seems more like proper magic.

Rational argument has only a limited role in establishing or destroying faith in Deities. Emotive and peer pressure forces have a far greater effect, and all religions employ both although the emotive hooks used by religions or sects within religions can change and evolve with time.

A previous blog discusses the emotive tone of what Richard Dawkins called ‘The World’s Second Worst Religion’ the one that has relied heavily on ‘Guilt and Self-Righteousness’ duality: -

That perhaps now shows signs of improvement under a new Pontiff.

However  if you tried to devise the most ghastly and most destructive possible emotive tone for a religion or sect, then a duality of ‘Self-Pity and Mercilessness’ would fit the specification perfectly and result in The World’s Worst Religion.

Robo-Stogie. The benefits of nicotine seem substantial. Chain-smoking through self-administered Mensa IQ tests seems to add ten percent to my score. Nicotine also gives you at least a couple of yards advantage in an emergency brake whilst driving. (Although for reasons of absent mindedness, apophenia, impulsiveness, ecology, and a preference for exercise, I have always declined to drive.) Nevertheless after fifty years of tobacco enjoyment my dentist said it wasn’t doing my teeth any good, so I went over to Vapes. These seem absolutely brill, cheap to run, thousands of exotic flavours to choose from, no danger of setting your bed on fire, little sign of use or offense to others if you don’t exhale quickly, and probably no personal or collateral damage, assuming that propylene glycol remains as harmless as it seems.

Many thanks for all the emails appreciative of the neo-classical statuary. The next project may consist of designing some ornate bronze rams for the prows of our Trident nuclear submarines. Comrade Commissar Corbyn has come up with the cunning wheeze of disarming them but keeping them to create employment. So if they cannot carry effective weapon systems they should at least carry aesthetically pleasing ones, in a Corinthian or Athenian style perhaps?

Monday, 21 December 2015 18:49

Winter Solstice Address 2015.

Winter Solstice 2015.

The year ends on several hopeful notes. The Paris Climate Conference has at least resulted in an agreement about the reality of anthropic climate change and the need to prevent it, so two cheers for that. However we should have had a result like this a decade or more ago and effective measures in place by now. Whether or not the recommended measures become implemented and whether or not they can save global civilisation remain open questions. This planet already has a human population level lying terrifyingly in excess of long term sustainability levels even at current rates of resource destruction.

If we wish to avoid a 21st century characterised by resource conflicts, environmental degradation, constant wars and extremist political and religious ideas, we had better fix our climate changing behaviour and our population and consumption levels, because at present the figures for the future simply don’t add up………….to anything except disaster.

The British people should will finally get a referendum on the EU, this coming year or the next, another cheer for that.

UKIP has fulfilled its function, it has forced the other parties to offer a referendum, and now, win or lose, UKIP seems to have little further use. It only ever had one worthwhile policy and everything else seemed like buffoonery. Yet I feel justified in having worked for them in their early years, for now we get to answer the question that most of the political class didn’t want to even ask us: -

Do we wish to remain part of the creeping synarchist totalitarianism of a corrupt, mega-bureaucratic and undemocratic EU that favours only the political class and big business; or do we prefer freedom and democracy?

Any nation that trades its political independence for economic gain will end up losing both, as so many of the smaller nations in the EU have already discovered.

The EU stands built on bluff, fear, lies, and deceit and faux-internationalism. We would lose nothing and regain much by leaving, and Brexit may well bring down the whole rotten edifice.

On a more festive note I have made two seasonal gifts for my fellow humans, firstly a lifesize statue of Hercules who will go on extended loan to some semi-public gardens around here to celebrate the several years of backbreaking toil we have put into renovating it.

Secondly, after two decades of mental toil the Hypersphere Cosmology hypothesis has probably reached its final form, see the recently updated version here: -

and full paper here: -

My thanks to all those physicists, both orthodox and alternative, who have exchanged so many emails, criticisms, observations, and related ideas on this subject. The hypothesis now seems reasonably robust and anti-fragile, but please do try to break it if you can, or if not then try challenging your commanding professor with it.

Historical accident has led to the current dominance of the Lambda CDM Big Bang theory. Perhaps if we had discovered the CMBR before we discovered the Cosmological Redshift then Einstein might have stuck with his Riemannian Hypersphere model of the universe with a cosmological constant, and looked a bit further into the properties of the hypersphere to find that he could have stabilised it with a cosmological constant supplied by a 4-rotation (rather than a Gödelian 3-rotation), and that the positive curvature of the hypersphere would itself  create a cosmological redshift without any expansion at all. All other observations could then have become interpreted within such a framework to yield a theory such as this.

It may not turn out as the final answer in cosmology but it certainly seems less wrong than the current official model. If nobody manages to falsify it, I shall devote my remaining years of theoretical endeavour to modelling quantum fundamentals and particle physics in terms of three dimensional time, plus of course the related and more difficult matter of a general theory of magic.

At Grove last night many spoke of the Winter Solstice as marking the end of the year, and how much they looked forward to the return of the Sun (despite that so far we have had the mildest winter here for thousands of years). The great megalithic monuments such as Stonehenge, Maes Howe, and Newgrange all plainly align to the Midwinter Solstice, despite that Druid-revivalists tend to look to Stonehenge at the Summer Solstice, and that the megaliths originate from pre-druidical cultures anyway.

But what the heck, all cultures in temperate latitudes seem to evolve some excuse for an end/beginning of year party. The Christians, having no clue about the actual birthday of their saviour decided to slot it in on 25th December to try and supplant Pagan festivals at that season, Mithras’ birthday in particular fell on 25th December. However by this date the sunrise and sunset have started to perceptibly march north again bringing hope of summer and rebirth and all that sort of thing.

Personally I like to consider Winter Solstice as the end of the year, a time to look back on events and then to look forward to Xmas as a celebration of Family and Friends and Commerce, (oops that should have read ‘The Bounty of the Earth’), and then again to celebrate New Year……..sort of Look Back, Look Now, Look Forward.

All the best for the festive season. Pete Carroll.

Addendum 29/12/15. Contrary to widespread rumour, the destruction of Boleskine House (The dread Kaaba of Crowleyanity) and my seasonal visit to Inverness remain not even coincidental. I did indeed visit my eldest in the surrounding highlands over the xmas period, however I arrived there on xmas eve, as my airline booking clearly demonstrates, to find the place already burnt down a day in advance of my visit. 

Wednesday, 09 December 2015 14:56


A pre-solstice blog.

A bit of an interregnum prevails before the festive season. The Knights of Chaos have launched their conjuration in support of the Climate Change Conference in Paris. The festive gifts and cards await dispatch, the Solstice Grove and Eisteddfod loom, and later my clan will gather in the Scottish Highlands this year.

On Arcanorium we prepare to invoke Venus in her many forms, as the first of a sustained series of planetary style workings based on the EPOCH. This seems particularly apposite for the season of love and goodwill towards all creatures.

A new Hypersphere Cosmology 2 paper awaits the attention of my artist and IT friend before it appears here and on viXra.

Whilst waiting for the paint and the sigils to dry on the 54 Lamens of a new Epoch Astronomicon and for the composites to harden on the new lifesize Hercules statue for the gardens, Azathoth and Yog-Sothoth provoke further musings upon the hypothesis of 3D time……

This very long term 3D time project seeks to complement the Hypersphere Cosmology thesis which now nears completion, and to make some conceptual improvements and revisions to the Standard Model of particle physics and to quantum fundamentals which currently look very messy, full of seemingly arbitrary constants and short on unifying principles.

The Standard Model predicts that a Higgs Mechanism accounts for some of the mass of mass bearing particles and that the presence of a ‘Higgs Field’ to endow such particles with mass implies that a Higgs particle (the Higgs Boson) will exist. However this flies directly in the face of General Relativity which describes mass as arising from/as spacetime curvature. The General relativistic description works very well indeed although it may require a tweak or two at very high intensities and at very long distances as suggested in Hypersphere Cosmology. The Higgs idea also flies in the face of the hypothesis of 3D time which seeks to geometricate the quanta rather than to quantise gravity.

Plus adding a Higgs Field to the standard Lambda CDM cosmology model looks like creating an even worse mess.

The purported Higgs Mechanism does not seem to even half quantise the inertial or gravitational manifestations of mass, for the Higgs field or boson would have a different coupling constant for each type of particle that it supposedly confers mass upon.

Thus I have volunteered to eat the relevant pages of The Octavo in the event of the discovery of the Higgs Boson. Why have I not done so then?

Because I don’t think that little blip in the data at 126GeV indicates a Higgs Boson or a Higgs Mechanism at all, I remain completely unconvinced.

After spending many billions of euros on building the largest most expensive scientific instrument in human history and failing to get anything spectacular or decisive out of a series of exceptionally messy experiments designed by huge Euro- committees, CERN felt under intense pressure to announce something; even if it meant highly selecting the data and then torturing the remaining data statistically till it yielded the appearance of a significant result.

The graph shown here gives a plot of selected proton collisions at various energies which produced a pair of detected gamma ray photons which may have come from a Higgs Boson which itself remains undetectable because it decays almost instantly after its creation.

Note that pairs of gamma ray photons get produced at a large range of energies, the apparent slight peak of them at around 126GeV apparently indicates something of immense significance, the other small anomaly at around 138GeV gets ignored.

Other experiments seem to show slight blips in the numbers of pairs of Z bosons at roughly similar energies.

Despite that the CERN team assert that they have 99.999% confidence that they have found something slightly anomalous at around 126GeV that might correspond to a Higgs Boson, and that the popular science press confidently proclaims the existence of what they have dubbed ‘The God Particle’, the internet and the scientific journals remain alive with dissent.

See this from a worried statistician

If the CERN team had conducted similar experiments and statistical analyses with the aim of disproving the existence of significant evidence for a Higgs Boson at these energies they would have succeeded. It remains a theoretical construct in my view, and probably a fallacious one at that.

Why do I care?

I love Science. If the Higgs turns out as a fudge created by a huge committee then many will interpret it as institutional fraud on a vast scale which will have a very detrimental effect on the perception and funding of science.

I love Metaphysics. The quest for the underlying structure and functioning of this mysterious universe never loses its fascination.

I love Magic. A largely dismissive attitude to magic generally prevails and this suits me fine as I therefore cannot get arrested for it. However any general theory of magic will probably require 3D time.  

Wednesday, 18 November 2015 21:05

Unknown knowns

The three Mandragora Autumnalis roots awoke around Samhain as usual to produce green shoots, so now after their repotting they reside on a window ledge soaking up the faint autumn sunshine. Perhaps the largest one will flower and produce some seeds this year; they certainly seem to take their time about it.

We serious British pagans don’t do Halloween, that awful American tradition of teaching children to extort with menaces and mock at Death. We do Samhain respectfully on the closest Sunday evening.

Bonfire night passed with a splendid conflagration which did not include an effigy of the Pope this year, as for the first time in centuries we seem to have a decent bloke in the post.

Meanwhile a life size statue of Hercules takes shape in the garage using the old clothing mannequin and Jemsonite trick. He will eventually stand with Flora, the pair flanking an old rustic doorway in the walled garden. He will have a spade and a chainsaw as a modern touch. Pic to follow eventually.


And now to some “Unknown Knowns”. Stuff we don't realise that we already know. This Apophenic concept takes its inspiration from the missing part of Rumsfeld’s Theory of Known knowns, Known unknowns, and Unknown unknowns. (His excuse for the screw up in Iraq.)

We probably already have more than enough of data and theories from which we could distil a much more accurate and useful description of the universe. However the trick lies in intuiting what to select from it all, and how to interpret the bits which apparently don’t fit in a way that they might.

Why do this? Why write The Octavo? What the heck has magic and esoterics got to do with cosmology and quantum physics?

Perhaps everything: - The Natural Philosophers and Wizards of old did not shy away from science in terror of the mathematics, rather in pursuit of a philosophy of nature in its entirety they sought to leave nothing out. Hermes Trismegistus (who may have consisted of a committee), John Dee, Giordano Bruno, Paracelsus, Isaac Newton and all the rest of them, took a keen interest in the workings of the material world and only the most myopic of contemporary quantum and cosmological physicists fail to muse and speculate upon the metaphysical implications of their disciplines.

A Speculation: - Hypersphere Cosmology depends on spacetime curvature. The hypothesis of Three Dimensional Time depends on torsion (spin). Einstein-Cartan theory includes both curvature and torsion. EC theory remains unfalsified and in play, though few theorists reference it today, except perhaps to remove the nonsensical spacetime singularities that arise in the conventional big bang theory and in the black holes that straight general relativity predicts. Instead EC theory proposes that mater particles have a minimum size rather than a point like nature and that they resist compression beyond this, so instead of a big bang singularity we may have a universe which bounces back and forth between a very small and a rather large size, yet the theory does not usually get used to eliminate ‘ordinary’ black holes, although it does eliminate possible pesky little black holes of less than 1016kg, the mass of a substantial asteroid.

In EC theory, particles have a spin or torsion component which gives them a minimum spatial displacement, the Cartan Length lCA.

Where lCA3 = Gh2/mc4 where h = Planck’s constant.

Interestingly, we can decompose the Cartan ‘volume’ lCA3 above into: -

Cartan volume = Planck area (Gh/c3) x Compton length (h/mc)

And/or/or possibly both…….

Cartan volume = Compton area (h/mc)2 x Hypersphere length (Gm/c2)

(Note that hypersphere length lH differs from hypersphere external radius r,( lH = pi r)

These components may in some way correspond to the wave/particle duality and can confirm that particles do indeed have some kind of hypersphere properties.


Another Speculation: - Hypersphere Cosmology seems capable of explaining quite a lot of the structure and behaviour of the universe using rather different assumptions and interpretations of the data than the popular standard Lambda Cold Dark Matter Big bang theory uses. Both approaches still have their problems and require further modifications before we can tell which seems the least wrong.

Hypersphere Cosmology has taken flak over the issues of Metallicity and Black Hole build-up.

Basically cosmologists refer to all the chemical elements heavier than hydrogen (and sometimes helium as well) as ‘metals’ as most of them have metallic qualities. These elements get formed in stars by nuclear fusion (although according to BB theory a lot of the helium got made at the BB.) Now if stars continually fuse hydrogen to heavier elements and no mechanism to break those heavier elements back down exists, then the Perfect Cosmological Principle implied by a finite and unbounded universe hyperspherical in space and time that should appear pretty much the same on the large scale at all points in space and time, seems violated.

The Perfect Cosmological Principle also becomes violated if all the matter in the universe will eventually become sucked into black holes from which it can never escape.

Several observed and hypothesised phenomena may solve the metallicity and black hole problems.

Neutron stars almost certainly exist. Metallic elements falling into neutron stars will get broken back down into neutrons. Neutrons which escape into space rapidly undergo beta decay creating electrons and protons which recombine eventually to form hydrogen. But can they escape?

Pair-Instability Supernovae may well occur. In these events the gravitational collapse of a sufficiently heavy star results in a very powerful gamma ray flux in the core. The gamma rays interact with matter particles initiating electron-positron pair production; this causes the pressure to drop in the core and further collapse to occur. This initiates electron-positron (matter-antimatter) annihilation which explodes the star completely into space leaving no remnant core. Astronomers have observed several possible examples of such an event.

Neutrons may act as Marjorama rather than as Dirac fermions under extreme conditions. In other words they may act as their own antiparticles and annihilate to gamma rays under conditions of extreme compression and temperature.

We do not know what mechanism creates Gamma Ray Bursts, but about once a day one goes off somewhere in the universe. These titanic GRB explosions appear to liberate the energy equivalent of the masses of entire planets or entire stars in brief moments.

Massive and very dense objects of multiple solar masses seem to exist in the universe and most galaxies appear to contain objects of thousands or millions of solar masses at very high densities in their cores. Whether any of these objects have actually formed black holes remains undecided. The maths breaks down at black holes and we cannot directly observe them.

Black holes may not actually exist at all if some mechanism like the above or perhaps some other mechanism limits their maximum density and consigns them to eventually explode, recycling the matter of the universe.


Lastly: - Whilst musing upon ‘Theory of Mind’ it occurred that perhaps Autistic people would not suffer from The God Delusion.

If the god delusion arises from the application of Theory of Mind to find agency or mind or essence not just in people but also in inappropriate phenomena or basically everywhere; and if Autistic people don’t make much use of Theory of Mind, then one would expect Atheism of them.  A quick googling of the topic confirmed this hypothesis in general terms.

Perhaps we Chaoist-Neo-Pagan-Pantheists have a surfeit of theory of mind, we tend to see multiple sources of agency even within ourself(s)!  


Tuesday, 20 October 2015 08:44


Into the Darkness.

The last late Dragonfly of the season took to the air above the pond at Chateaux Chaos a week ago. She hovered around planting her eggs in the moss and weeds. In three years’ time her children will emerge having gorged themselves on the toadpoles in the depths.

As the evenings draw in, and the nights become chill and clear, it seems time to prepare poetry for the Samhain Eisteddfod, to invoke the Elder Gods, and to return again to cosmological questions.

Standard conventional Big Bang Cosmology depends on the idea of an expanding universe, and the fairly recently observed mismatch between the redshifts and the luminosities of type 1A supernovae has led to the further twist that the hypothesised expansion of the universe has apparently progressively speeded up during the last half of its expansion to date.

Despite the manifold problems with all versions of the Big Bang theory, and its general metaphysical distastefulness, it seems difficult to find papers on cosmology that do not automatically assume that we inhabit an expanding universe and which try to interpret all observational data accordingly.

However an interesting exception occurs here

The ‘Angular Size’ of structures in the cosmos may give some indication of the geometry and topology of the universe in space and time. Many models based on expansion predict that structures at very great distances in space (and therefore time), should appear magnified because of the subsequent expansion.

Hypersphere Cosmology also predicts the magnification of very distant structures, but for a different reason. In Hypersphere Cosmology the small positive spacetime curvature of a non-expanding (vorticitation stabilised) cosmic hypersphere will exert a lensing effect which will not only magnify very distant structures but which will also diminish closer structures. This diminution of closer structures will create the optical illusion of a universe which appears to have undergone an accelerating expansion during the last half of its expansion to date, if observers wrongly assume that they look out over a gravitationally ‘flat’ universe.

In the graph below the horizontal axis, (shown marked with 1 billion light year divisions) stretches from the observer at the origin to the limit of observation which corresponds to the hyperspherical antipode distance in Hypersphere Cosmology. We have used the figure of 13.8 billion light years here. The actual distance may differ slightly from this; we await a more precise measurement of the Anderson deceleration or the undistorted Hubble distance.

(GM/L^2 = A, where G = Gravitational constant, M = Mass of universe, L = Antipode distance which corresponds to Hubble distance, A = Anderson deceleration which corresponds to the spacetime curvature.)

The vertical axis for a number of factors runs from zero to three, marked in divisions of 0.5 with the unity line highlighted in purple for clarity.

The red line shows redshift Z, where Z = (c/(c-(dA)^0.5)-1 where d = astronomical distance.

Note that a redshift of 1 at about 7 billion light years denotes the halfway point to the antipode distance. Redshift climbs exponentially towards infinity at the antipode; observations become increasingly difficult up to redshift 10 and then virtually impossible beyond.

The yellow line represents schematically the hyperspherical geodesic from the observer to the observer’s antipode; the curved path that light actually takes in the cosmic hypersphere.

The blue line represents schematically the observer’s assumed sight line for flat space.

The green line represents schematically the difference between the actual and the assumed sight line, and thus the degree of Hyperspherical Lensing LH, that light becomes subject to at various distances. Note that in this revised version of the model, the line has the inverse configuration to previous models on this site and the equation governing it has the form

LH  = 1/(1+((d-d^2)^0.5))-d) where here, d = astronomical distance/antipode distance.

The negative lensing at distances below 7 billion light years explains the anomalously low luminosity of type 1A supernovae without recourse to the hypothesis of an accelerating expansion driven by some mysterious dark energy.

The positive lensing at distances greater than 7 billion light years explains the increase in angular size of very distant structures without recourse to the hypothesis of an expanding universe at all.    

Monday, 28 September 2015 10:42


My thanks to all participating Knights, Dames and Squires of the KoC, and to all participating allied magical support. Thank you for your conjurations.

Herewith our next target:-


Monday, 21 September 2015 20:48

Magical Questions

Having returned from Cyberpurdah in deepest Wales I notice that Comrade Corbyn got elected as labour leader. Splendid, the labour party can now return to doing what it does best, providing opposition and nurturing grievances and introducing young people to the extremities of ideological debate. Hopefully we shall not see it in government exercising its customary economic mismanagement for some long while yet. Now that the UK conservative party has adopted social liberalism, the labour party has only fiscal fecklessness left to offer.

Anyway, to the more significant questions of Esoteric and Magical Theory.  

Some people seem to think that they basically know everything about magic now so they have nothing left to research or to teach.

I get mad at this and assert that we still don’t know a fraction of it, and so herewith a few of the things that remain unanswered or unasked.

I should point out that I consider that the whole universe runs on magic but the bits of magic that work fairly reliably we now call science; so I’ll try to confine myself to the bits of magic that work rather unreliably and which we still call magic.

The World

The Tree of Life gives a map of the solar system, so one up to the wizards for anticipating the planets beyond Saturn, but our kabala doesn’t look big enough now.

What about the geometry and topology of the whole cosmic caboodle?

Do we have room enough for the other worlds of Giordano Bruno?

Or the Mad Indifferent Demon Gods of HP Lovecraft?

Do we treat the Space Gods as incarnate, discarnate, or imaginary?

Can we communicate with them by quantum telepathy or whatever, can we specify?

The Future

Do we divine the future states of reality directly, or do we divine our future experiences of them? (We could devise tests for this.)

Should we enchant for direct effects on reality or should we enchant to enhance our mundane abilities to get those effects?

The Past

In what form does the past persist? In memory, in records, and in physical traces obviously.

But what about in the aether, in the astral, in morphic fields, in the akashic records or whatever wizards call the stuff?

What do we actually get when we try out antique gods, ancestors, and necromancy?

The Pasts Plural

The future seems to open like a garden of forking paths of various probabilities.

Does delayed choice quantum erasure and retroactive enchantment suggest many paths behind us also?

A garden has a width as well as a length. Does time have a sideways as well?

The Presents

Do we exist in and as an interference pattern between all the possible pasts and futures?

Does consciousness consist of a superposition of several states at once?

I find myselves in two minds about this.


Stuff plainly develops properties and behaviours which don’t seem inherent in its component parts.

The Universe exhibits Imagination.

For example: -

Hydrogen consists of a colourless odourless gas that slowly turns into people, - if you leave enough of it lying around for long enough.

Emergent phenomena seem to slip out between the interface of deterministic and random behaviour, from between order and chaos, and take on a life of their own, raising BIG magical questions: -

How much top down causation (or chaos) can emergent phenomena exert on their component phenomena?

Do we inhabit a Panpsychic Universe?

Can an apparently emergent vitalism or life force have real effects?

Does Chi or Vril or Prana or whatever you call it, meaningfully correspond with anything to do with ‘Energy’, or does it correspond more to something like ‘Intent’.

Does the apparently emergent ‘Self’ have real effects, or does our emergent free will remain largely subconscious?

How far can we take the idea of Magic as The Real Effects of Imaginary Phenomena? (Imaginary in the psychological sense, and Imaginary in the sense of orthogonal time vectors.)

Ars Notoria

Does this much maligned and frequently ignored magical art actually offer the possibility of inspiration to learn all sorts of knowledge in support of a magical quest?

Style and Technique

Psychedelic autognosis can reveal the self as a contingent construct, the subconscious as a well of creativity, and the belief system as somewhat reprogrammable. Yet these things should occasion the Buddhist or the magician no surprise. Psychedelics seem unsuitably imprecise and dangerous for work in psychotherapy or psychiatry. The idea that societies have generally banned them out of fear of mass enlightenment seems undone by the observation that massive illegal use has not had this effect.

Did a whole generation get taken in by the sixties myth and marketing hype that psychedelics could confer mystical and magical powers?

Does Apophenia serve as a more suitable goddess for magicians than Eris? 


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