Blog (244)

Thursday, 29 October 2020 19:31

Samhain 2020

Samhain 2020

Magical Attack

Now seems the time to throw in some Sorcery in support of all the mounting Scientific attacks on Covid 19, if some form of vaccine can work then we can perhaps avoid a grim Fimbulwinter.

Local Midnight 31st October, prepare for a coordinated conjuration: -

1) Dress a seasonal pumpkin with spikes suggestive of the coronavirus.

2) Lay out weapons of choice.

3) Gnosis – attain mental focus either by silencing the mind with meditative procedures or by exciting the mind to frenzy by exertions and wild emotions.

4) Physically wreck the symbolic image of the target without conscious deliberation.

5) Banish with deliberate laughter and thereafter avoid thinking too much about the conjuration.

Ouranian Barbaric or Enochian incantations, sigils, nudity, or robes and black pointy hats optional.

Personally, I shall use a Hammer of Thor, an original Tibetan Purba, and all three manifestations of the current Mk127 pocket wand.

Received from Japan

This curious and rather beautiful object, thoughtfully incorporating a personalised nameplate. It glows in the dark as well, a desktop or bedside wand/chaosphere always at the ready and easily accessible in pitch darkness.

Hyperspheres in the Microcosm

Lastly, as part of the ongoing Quantum Hypersphere Mechanics project. A contemplation of Mobius strips with half twists in them: -

Suggests that spinors may arise from a hyperspherical rotation, consider an object with axes x, y, z, and a fourth-dimension w, it can have 2 independent planes of rotation, say xy and wz.

An 1800 rotation about wz will invert the z axis about which the plane of xy rotates and a 3600 rotation will restore the orientation of the z axis, but this will entail a 7200 rotation of the observable xy plane! Such non-isoclinic (not equal angled) rotations of 4D spacetime quanta may explain a lot.

Wednesday, 21 October 2020 19:55



Pandemic lockdown has provided an opportunity for something of an Annus Mirabilis in metaphysical magical theory and The Occultaris* proceeds apace: -

                                       TIQM + HM + WSM + HC = OM!

Basically, an Apophenic addition of Cramer’s Transactional Interpretation of Quantum Mechanics, (for energy quanta), to Hypersphere Mechanics to Wolff’s Wave Structure of Matter, (for matter quanta), to Hypersphere Cosmology, (in eight-dimensional spacetime), yields an Omnality Matrix, partially entangling absolutely Everything, this seems metaphysically satisfying and has extensive explanatory and predictive power in both parts of Natural Philosophy – Science and Magic.

In response to questions about particle generation/flavour conservation in the previous blog: - The decay of higher generation quarks does not appear to conserve particle generation. However higher generation quarks only arise as entangled quark-antiquark pairs and a consideration of the decay products of both the quark and the antiquark reveals a perfect conservation of particle generation/flavour quantum number.

If generation remains conserved and baryons consist of uni-quarks then an 8-dimensional hyperspherical universe with quanta having 4 rotational degrees of freedom becomes an increasingly credible sub-quantum epistemology, and perhaps even an ontology and a metaphysic.

*Book to appear eventually…………….

Gardening and Board-Gaming/Building meanwhile continue to provide light relief from the mathematics.  

The Mandrakes at Chateaux Chaos sprouted early this year at the autumn equinox. Their roots had become too big for their individual pots so now they reside together in a single deep and huge one. Hopefully, they will all produce some apples this winter, not just Circe the big one.

Updates to Frontier Space War 2.

The scenarios have evolved through further playtesting: -

1) Discs placed below pieces indicate the number of units of that type, but the number of groups of any type of piece remains restricted by the number of pieces.

2) Command Vessels: - Tactical Attack/Defence use next dice up in size. Psi Attack/Defence best of three dice throws. This proves much simpler than adding numbers to dice throws.

3) Fortresses all use D12 Dodecahedrons A/D unless enhanced by a Command Vessel.

4) Strange Aliens. (partly inspired by the current plague)

Aliens have just two types of units, Hives and Wasps. Wasps can move from one system to another connected adjacent system each turn, and attack or defend with D10 Decahedrons. Hives cannot move and have no attack or defence capability and become destroyed by any attack. Hives can produce Wasps at a cost of 4 production units. Wasps can turn into Hives and vice-versa.  A newly created Hive cannot create Wasps in the same turn it became created, but a Hive that turns into a Wasp can move and attack in the rest of the turn.

Possible scenarios including Aliens.

1) Aliens use the Soviet Territories in place of the Soviets. They start with a Hive on Vostok.

2) An alien force of 5 Wasps can appear once at any Black Hole between any two other Faction’s turns, at the discretion of the Alien commander who then takes that turn for the rest of the conflict.

These Alien pieces consist of black Milliput over nuts and bolts, gone over with black felt tip marker to give them an eldritch organometallic sheen.

Brexit appears to proceed well. We should not negotiate. David Cameron and Teresa May both attempted to negotiate and they both failed and got sacked. We should simply say what we intend to do and do it, and that includes not imposing barriers or tariffs unless they do.

Saturday, 19 September 2020 10:18

Particle Physics Police

We invite the Particle Physics Police to falsify the following hypothesis before our Geometric Algebraists endeavour to take it any further.

It may form part of the forthcoming Occultaris, a Natural Philosophical investigation of the Macrocosm and the Microcosm.

Hypersphere Mechanics.

The conventional Standard Model of Particle Physics and the accompanying (Standard?) Copenhagen Interpretation of Quantum Mechanics plainly remain incomplete models of the Microcosm that do not penetrate to the bottom level of reality.

Hypersphere Mechanics models both particle Physics and Quantum Physics exclusively in terms of the same dynamical Spacetime Geometry that describes the Macrocosm in Hypersphere Cosmology.

Conventional Quantum Mechanics models the nuclear force as having a threefold symmetry whilst using twofold symmetries for particle spins, electromagnetic charges, and particle generations. Hypersphere Mechanics uses twofold symmetries throughout, and it equates all four particle properties to spinorial rotations of four planes in eight-dimensional spacetime.

Hypersphere Cosmology explains the Universe in terms of a Vorticitating Hypersphere consisting of curved 3D space in time and speculates that time may also have a hyperspherical geometry. 

A Hyperspherical universe finite but unbounded (closed) in both space and time, also implies curved time.

Two extra orthogonal time dimensions can explain quantum superposition and entanglement and the probabilistic behaviour of observed reality.

If the universe exists as a hypersphere in both space and time, then it has 8 dimensions.

A spacetime of n(even) dimensions has n/2 possible rotation planes. ((n-1)/2 for n(odd)).

(a 3D spatial ball has only one rotation plane, trying to rotate a rotating ball about another plane merely changes the rotation plane to one at a different angle as per the quaternion rules.)

A four-dimensional object such as a hypercube can have two independent rotation planes, the Clifford Double Rotations, such as wz and xy, or indeed any two rotation planes such as wx and yz.

A ‘quantum of spacetime’ can rotate in 8 dimensions and it can have 4 independent rotation planes: -

In spacetime, a rotation of plane consisting of a spatial direction and the spatial curvature represents a direction of travel along the spatial direction. In spacetime, a rotation of plane consisting of a temporal direction and the temporal curvature represents a direction of travel along the temporal direction.

In hyperspherical Spacetime of w xy z space, and of a bc d time,

w denotes spatial curvature (as a magnitude component in the vector representation); z denotes particles direction of spatial travel

a denotes temporal curvature (as a magnitude component in the vector representation); d denotes particles direction of temporal travel.

If we regard the curvatures w and a as unobservable and the directions z and d as observer dependent, then we can denote the 4 spin planes as: - wz,  xy,  ad,  bc.

As spins have quantisation then perhaps, we can expect spins like +xy, -xy, +2xy, etc.

All planes rotate Spinorially - their rotation puts a twist in the surrounding space or time which untwists with a full 7200 rotation. Such twists create attractive or repulsive fields, and spacetime itself.

Particles and their component spins.

± denotes plus or minus

≠ denotes plus and minus, spins of the double component Bosons which cancel each other but which nevertheless carry energy.                          


                     Chiral Spin               Nuclear                     Electric                 Generation

                         ±xy                          ±ad                            ±bc                          ±wz


Dirac Spinor Fermions   +xy+wz   -xy+wz   +xy-wz   -xy-wz   Electrons and Quarks.

Weyl Spinor Majorana Fermions   -xy+wz   +xy-wz   Neutrinos only.


Fermions. All with chiral spin ±1xy. (±½) in conventional notation). All antiparticles have reversed spins.

                      Chiral Spin               Nuclear                   Electric                      Generation

Neutrino           -xy (-½)                  -                              -                             +1,2,3 wz (e, μ, τ)

Electron            ±xy (±½)                -                             -bc                          +1,2,3 wz (e, μ, τ)

Quark d type    ±xy (±½)              +ad                             -                          +1,2,3 wz (d, s, b)             

Quark u type    ±xy (±½)              +ad                          +bc                         +1,2,3 wz (u, c, t)         

Baryons            n&±xy ±½ etc       +ad                    0, +bc, +2bc                 +1,2,3 wz

Proton = u type quark. Neutron = d type quark.


Bosons. All with chiral spin of 0 or 2 (2=1 in conventional notation.)

                   Chiral Spin               Nuclear                   Electric                      Generation

Graviton        ≠xy (0)                    -                         -                                        wz

Gluon            ±2xy (±1)                ≠ad                                                               wz

Photon           ±2xy (±1)                  -                                                                wz

Z Boson         ±2xy (±1)                  -                           ≠ bc                               wz

W- Boson       -2xy (-1)                   -                           - bc                               wz

W+ Boson      +2xy (+1)                  -                          + bc                               wz

Mesons        n& ±2xy or ≠xy        ≠ad       0 or ≠bc, or ±bc, or ±2bc        various q/-q

All bosons have a ‘particle-antiparticle’ nature.

The Graviton thus consist of a zero-spin neutrino-antineutrino pair. The Z boson consists of an electron-antielectron pair with aligned chiral spins. The W bosons as electron-antineutrino or antineutron-neutrino configurations with aligned chiral spins. The component parts of Gluons, and Photons, do not exist independently. Mesons consist of various uni-quark baryon/anti-uni-quark anti-baryon pairs and come in many forms.

Bosons that do not displace wz time, remain free from the Pauli Exclusion principle, allowing them to form unlimited fluxes

Chiral spin and generational spin can interconvert with orbital angular momentum or velocity, and hence do not invariably conserve.

Nuclear Charge has a twofold symmetry not a threefold symmetry. It exists in ± form, not in a threefold colour/anti-colour form. Protons and Neutrons exist as fundamental uni-quark fermions. The Proton carries nuclear charge and electric charge, the neutron carries nuclear charge but no electric charge. At a stroke this removes the idea of fractional electric charges and all the complex confusion of QCD, (Quantum Chromodynamics). Mesons still consist of all the quark/anti-quark pairs as in conventional theory. Moreover, it makes everything consistent with the overall twofold symmetry implied by simple ± plane rotations. The +ad+wz or -ad-wz nature of quarks may represent another Weyl Spinor, or it may result from alignment of spatial and temporal directions of travel.

The whole array of short-lived Exotic Baryons and Baryon Resonances becomes explicable in this Baryon = Uni-Quark model: -

                   Chiral Spin               Nuclear                     Electric                 Generation

Baryons        n& ±xy                    +ad                    0, +bc, +2bc                 +1,2,3 wz


Mesons have an overall angular momentum composed of the intrinsic angular moment of the quark-antiquark pair, ±2xy (=±1) or ≠xy (=0) plus the quantised orbital angular momentum of the two quarks around each other (denoted above as n&) of ±1,2,3 etc, to yield integer spins.

Baryons as uni-quarks have an overall angular momentum composed of the intrinsic angular momentum of the quark ±xy (=±½) plus a quantised rotational non-spinorial momentum (denoted above as n&) of ±1,2,3 etc, to yield half integer spins of ± 1//2, 3/2, 5/2, etc. The resulting degrees of freedom allow many possible varieties of distinguishable baryon particle, although only the Proton exhibits long term stability.

Early measurements of spin 3/2 Baryons played a large part in the erroneous attribution of a threefold symmetry to the nuclear charge and a tri-quark nature to the Baryons.

In general, the greater the number of spins a particle possesses the greater the energy it carries and hence the more mass and the lower stability that it exhibits, although the spins do not summate in a simple way to yield a simple algorithm for predicting masses. Chiral Spins as high as 5/2 or 7/2 seem indicated for some exotic baryon resonances. Particle generations beyond 3 do not seem forbidden by anything except huge energy requirements.

In the Hadron realm of Baryons and Mesons, a sort of Nuclear Chaos seems to reign - a sufficient concentration of energy can probably produce any imaginable type of particle, but with a lifetime inversely proportional to its mass.

Quantum Chromodynamics, the theory that quarks come in three ‘colours’ and that anti-quarks come in three corresponding  anti-colours and that Baryons such as the Proton and Neutron consist of quark triplets, appears as an unnecessary complication that obstructs our understanding. It arose as a scheme for ordering the massively confusing array of Baryons and Mesons observed in high energy particle collisions, but such a model brings with it a whole slew of ad-hoc fixes. In the QCD model, quarks suffer from ‘quark-confinement’ which prevents them from ever appearing in single form, they also suffer from Asymptotic Freedom in which forces become weaker at short distances and stronger at long distances. Gluons have to come in eight different colour combinations to explain the forces inside atomic nuclei, and quarks have to subtend very complicated arrangements of virtual quarks and gluons around themselves to explain the enormous discrepancies between the theoretically predicted and the measured masses of various quark combinations. These ad-hoc fixes seem little better than the now discarded hypotheses of epicycles and phlogiston.

Hypersphere Mechanics models particles in terms of SNEG, all particles consist of ‘snegs’ in spacetime. (chiral Spin, Nuclear spin, Electric spin, Generational spin.)

The proton represents the simplest and only stable particle with all four spins, it has the SNEG signature ½ 111. The Neutron consists of ½ 101. Other unstable Baryons can have higher numbers in their signatures. Suitable choices of SNEG signatures can model all observed Baryons and Mesons and their decay products.

And on a lighter note the Lithonians now have a Fleet Carrier. Fortuitously a larger block of ceramic insulation material washed up on the shore of this lockdown hideaway. The Lithonians come from a metal poor planet and use a lot of stone in their starships and the detritus on this beach seems rather metal poor as well. Discarded vape accessories make up most of the metallic components of the vessels.



The voyage of the Leif Erickson and the Garuda.

I would like to contact the people we had an extraordinary adventure with, in India around 1979.

A group of us built two boats in North Goa, the Leif Erickson, and the Garuda, and sailed them south. The boatbuilding took four months, so we set off rather late in the season. Both boats were about 30 feet long and based on the hulks of old rotten dugout riverboats that we bought. We added freeboard planking, outriggers, rudders, masts and sails, and rowing benches and oars that we constructed ourselves having replaced the rotten parts of the hulls with local wood and caulked them with local materials that the native fishermen showed us how to make. Each boat also towed a small dugout canoe for shore visits.

Both boats set off southwards down the coast hoping to round the cape to Sri-Lanka, but we had set off rather late in the season for favourable weather. Nevertheless, we had a couple of good weeks sailing, occasionally pulling into incredibly remote fishing villages for water and supplies, to the astonishment of the inhabitants. The ocean seemed idyllic, we saw turtles and flying fish and swam in the phosphorescence at night, but then disasters struck:

The Garuda hit a rocky offshore island partway down the coast, the crew survived but the boat did not. The Leif Erikson continued and then ran into a typhoon in the night somewhere off the Malabar coast. After a titanic struggle against the typhoon the Leif Erickson limped into Cochin harbour with most of its rigging wrecked. An hilarious scene ensued when a motor launch from the Cochin Yachting Club came to inspect our craft, having heard that ‘a British yacht had arrived’. ‘That’s us’, we said. They took one disbelieving look at the bedraggled hippies in their ramshackle vessel and made a swift exit.  We swapped the remains of the boat for a few crates of beer. After a few days, the group dispersed on their travels and we have not seen them since.

About 20 people became involved in various part of the boatbuilding and sailing, we would like to contact any of them with a view to exchanging memories and photos and maybe writing a book about it all.

They say that everyone on the planet lies no more than seven links of acquaintance away from anyone else, so if you know any of these people please send them this article, or if not please forward it to someone who you think might know of them.

Herewith a list of those names we can remember: -

Leif Erickson Crew.

Pete Carroll, Christine Hutchinson, Simon Dunsford (British), Lars Jorgenson, fisherman, (Danish), Alfonso Lerna, racing driver, Alvaro Dominguez, chess master, (Spanish), Satayabodhi (Dutch guy, sannyasin name) Tony D’Souza (Anglo-Indian)

Garuda Crew.

‘Herr Robert’ as we called him, (German) he had worked on cruise liners, and a German couple. ‘Saco’ (Indonesian) and a skilled Chef. Ralph (Australian)

It would be great to hear from any of you 40 years on.

Regards, Pete and Chris Carroll, This email address is being protected from spambots. You need JavaScript enabled to view it.   


I do not usually do verbal interviews online, I prefer the more leisurely medium of email interview as it gives more time to think, nevertheless I did become persuaded to do this one: -


You can tell that I would have preferred more time as I keep saying, Well…. Erm….


Meanwhile a team of mathematicians and physicists crawl all over the Hypersphere Cosmology chapter of the Occultaris, eventually to appear in book form.


Friday, 17 July 2020 20:50

The Occultaris

Eight years have elapsed since my last book. Correspondents and publishers have started to ask if I have anything else in the pipeline. I most certainly do, although I wonder if the world can or will entertain its exceptionally challenging hypotheses. Herewith the provisional introduction and contents.

The Occultaris. Magic and Natural Philosophy.

By Stokastikos, Peter J Carroll.

Ch1. (Intro) Natural Philosophy, and the Occluded Universe.

Natural Philosophy used to mean the investigation of the natural universe and all its secrets by any means possible. It used to include anything natural that we could observe from mechanical, celestial, biological, medical, to even apparently ‘occult’ phenomena.

The great quest of Natural Philosophy lasted from classical antiquity until modern times and its remit included the study of all things, although it tended to avoid the pitfalls of applying reason to Theology and Religious ideas.

Then beginning in the early modern period, Natural Science began to assert itself and ended up by just calling itself Science from the latter part of the 19th century onwards.

What distinguishes Science from Natural Philosophy?

 “All Science is either Physics or Stamp Collecting.” -  Ernest Rutherford.

With this bold statement one of history’s greatest scientists asserted that the scientific understanding of anything depends on developing an explanatory mechanism that we can do some maths and measurement with, and check against experiment or observation.

Chairs of Natural Philosophy still exist at some venerable old universities and today Physics Professors usually occupy them.

Despite doing a great deal of Natural Philosophy, including speculative metaphysics and alchemy on the side, Isaac Newton managed to put optics, and terrestrial and celestial mechanics into the fold of (Natural) Science and then much else followed and The Enlightenment blossomed. Eventually even the study of living organisms grew from the mere phenomenology of Natural History into the Science of Biology with the discoveries of Evolution, Biochemistry, and Genetics.

These developments tended to leave Natural Philosophy with all the phenomena, ideas, and questions that we could not develop mechanistic explanations or descriptive mathematics for, often because we could not concisely define or measure them. Thus metaphysics, consciousness, teleology, essentialism, and subjective experiences tended to remain there largely ignored or dismissed by Science.

Enlightenment thinkers dismissed Alchemy and Astrology, probably quite rightly, as proto sciences that did not work. Religious ideas and practices became viewed as having social and psychological functions only, with nothing useful to tell about the Natural Universe on the basis that nothing Supernatural exists. Anything that really exists falls into the category of Natural, no matter how astonishing or hidden, or improbable it may seem.   

Magical ideas proved particularly resistant to mathematical quantification and description by testable mechanisms. Magic thus tended to become regarded as an Unnatural Philosophy concerned with phenomena that do not exist because we cannot readily measure them or easily perform repeatable experiments on them.

However, the far reaches of Physics in the Cosmological and Quantum domains do not yet conform to Rutherford’s ideals. Both fields remain at the stamp collecting phase, we have collected masses of observations, but we have no convincing and testable theories of mechanism, we just have a series of conflicting and often mutually contradictory ad hoc explanatory schemes. Cosmologists present extreme speculations as established facts. As Landau quipped “Cosmologists are often in error but seldom in doubt.”

 Quantum physicists argue constantly about the nature of the underlying reality or whether an underlying reality even exists or even has a nature that we can perceive.

Magic suffers from its own problems; in antiquity, magical theorists tended to borrow heavily from Religious ideas for a metaphysic and a vocabulary to describe their ideas and practices. Today, analogies to science often become employed. As Ramsey Dukes observes; Pseudoscience has become the language of choice for modern magical thinking. ‘Quantum’ has replaced ‘Astral’ in the magical lexicon. Yet that does not seem entirely inappropriate because as the great quantum physicist Richard Feynman asserted, “Nobody understands quantum physics” either.

This book aims to advance the cause of Natural Philosophy, the great quest to understand the secrets of the Natural Universe, by combining insights from the Unnatural Philosophy of Magic with insights from the increasingly Unnatural Philosophies of Cosmological and Quantum Physics.

In the cause of rendering all three of these disciplines less Unnatural and more consistent with each other, this book will advance many radical proposals and unusual hypotheses with supporting evidence, mathematics, and some proposals for experiments and observations.

Two magical experiments performed within the last thirty years gave very strange results and initiated the lines of enquiry that led to this book. Over the course of a career one becomes accustomed to Enchantments (making things happen by magic) going awry, sometimes solid objects in the vicinity shatter spontaneously, or teleport unbidden, sometimes unwanted metrological or seismic events have occurred, but these two experiments relate to Divination (finding information by magic).

In one of the two experiments a group of about forty magicians gathered in an Austrian castle and after a week of varied rituals and preparations set out to scry the Big-Bang event in a coordinated mass dreaming experiment. At the time, the so called Big-Bang had very much captured the popular imagination and become the officially sanctioned scientific answer. Many paperback books and documentaries had appeared on the subject and some of the Chaos Magic practitioners present had even gone so far as to identify Chaos Magic as ‘Big-Bang mysticism’. Despite expectations, all those who reported a result reported that the universe of 13 odd billion years ago looked much as it does now on the large scale. This provoked a quarter century quest to understand why almost all Cosmologists thought otherwise and whether they might have misinterpreted their observations, and whether a better interpretation exists.

Magicians have always made maps of the cosmos to guide them in their endeavours. For a long while they remained content with the solar system of the sun and most of its surrounding planets, and kabalistic schemes which derive from or relate to that, with maybe a nod to the surrounding celestial sphere. The magician Giordano Bruno went to the stake in 1600AD partly for asserting that other stars had planets orbiting them and that those planets carried other life forms.

In the other experiment conducted in the West of England, a group attempted to scry the results of horse races using a modified Ganzfeld procedure. Experimenters would first set up an array of unusual or surprising objects unknown to the test subjects. These objects would all bear numbers that corresponded to the race numbers of horses due to participate in a specific race in the near future. The test subjects would then enter a sensory deprived Ganzfeld state with opalescent lenses placed over their eyes and soft light shone into them, and with white noise played into their ears by headphones. Test subjects strove to achieve a vision of whatever object an experimenter would dramatically present to them after the race, the object chosen would correspond to the winning horse. The test subjects had no clues about what such objects might consist of or what races they related to.

Fortunately, we wasted no money on betting because it rapidly became apparent that test subjects frequently achieved false positives. They managed to scry unknown objects in the array, but these often did not correspond to the winning horses.

These results raised profound issues of indeterminacy, psychism, and the nature of time which led to several decades of research into the properties of the quanta which supposedly underlie the whole of natural reality.

Magicians have always made maps or models of how natural reality works. Early ideas about the Platonic essences of things and elemental classifications of phenomena as relating to earth, air, fire, and water gave way to models based on the rays and emanations and the luminiferous aether of pre relativistic physics.

If we have almost got to the underlying fundamentals of Nature with our investigations of the quantum realm, then perhaps we can attempt the final leap which will necessarily include accounting for magical phenomena in rigorous rather than pseudo-scientific terms.

The final leap almost certainly implies that we abandon two long held popular ‘privative’ concepts. A privative concept means an idea defined by the absence of something. Thus ‘Death’ does not consist of anything except the absence of life (except perhaps in Discworld). We commonly regard ‘Space’ as merely the absence of anything between separated objects, and ‘Time’ as merely the intervals between events.

When Newton proposed the concept of gravity, the idea of action at a distance without physical contact remained problematical to many including Newton himself. The later addition of the idea of a ‘gravitational field’ merely buried the problem until Einstein realised that what we call gravity means curved spacetime. As Wheeler later neatly summarised it, “Spacetime tells matter how to move; matter tells spacetime how to curve.”

In Einstein’s General and Special Relativity, space and time do not exist separately but always in the combined form of Spacetime. Moreover, spacetime has a definite geometry, structure, and properties, it can become stretched or compressed or curved or stressed by the presence of mass and energy. These principles underlie both the conventional Big Bang Cosmology and its alternative - the Hypersphere Cosmology that chapter 2 will explain.

In some approaches to quantum fundamentals, the mass and energy of the quanta themselves consist of geometric distortions in the fabric of spacetime. Chapter 4 will explore the idea that the existence and all the properties and behaviours of fundamental particles may arise from the geometry of spacetime if it has just two more natural dimensions than commonly realised.

Magical theories also require some sort of a medium for effects which extend across space and time. Traditional ideas about ‘spiritual forces’ or astral planes or ethers have never proved particularly useful or satisfactory and the more modern idea of ‘magical energy’ implies little more than some substance that sometimes does what someone wants it to.

This book will attempt to show that a (curved) six-dimensional spacetime could account for the structure and behaviour of the entire macrocosmic universe, the existence and properties of all fundamental particles of the microcosm and their quantum behaviours of superposition,  entanglement, and apparent indeterminacy, in addition to accounting for the probabilistic nature of enchantment and divination in magic.

Our most astute futurologist provokes us with the thought that the quest of Natural Philosophy may lead us to dark places: -

"The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the deadly light into the peace and safety of a new dark age."

The Call of Cthulhu --- H.P. Lovecraft - 1927

Yet only a Promethean response to the Indifferentism and Hostility of the Cosmos towards our randomly evolved species seems to offer it any long-term chance of survival. To this end we must attempt to correlate the contents of our minds and voyage far.


Ch2. (Physics) The Macrocosm, Hypersphere Cosmology.

Ch3. (Magic) The Occult Universe.

Ch4. (Physics) The Microcosm, Hypersphere Mechanics, Reversible and Transverse Time.

Ch5. (Magic) Practical Metaphysics.

Ch6. (Psychology) The Anthrocosm.

Ch7. (Magic) The Human Condition.

Ch8. (Outro) A Life.

And now for something completely different - Circe’s Children.

It all began with seed provided by the Greek wizard Xarisal. After seven years slow growth in the chilly British climate, Circe, the largest of the three Mandrakes (Mandragora Autumnalis) at Chateaux Chaos, has produced a mandrake apple, a seed pod. I shall offer some of her children for adoption at the next Druidical Eisteddfod with a view to their widespread reintroduction to Southwest England and Wales over the next century.

Lastly, another addition to the lockdown sci-fi creations, a major upgrade to the Frontier Space War game system with multiplayer and solitaire options and multiple backstory possibilities including neo-modern political and culture war, Alien encounter, and a Dune-style neo-feudal conflict. See below in the games section.

Sunday, 28 June 2020 09:02

End June 2020

What has gone wrong with Britain?

I only vaguely remember the Hong Kong Flu during my teens in 1968-70. It killed more people than Covid has so far. Some services and facilities became temporarily disrupted but societies carried on without much fuss or lockdowns. The virus still exists but humanity has fairly good herd immunity to it now.

This current Pandemic has brought many issues into focus, in part because the now omnipresent media has had so little political or celebrity or sports news to report on.

However, we look at most of these issues the wrong way around.

We do not have a housing shortage. We have a population glut.

We have deliberately engineered this by allowing a net immigration of 300,000 per annum. This suits property owners fine; their properties inflate in value and this effectively acts as a massive tax on the young. Property has become a much more lucrative investment than industry.

Normally a ‘price improvement’ means something has got cheaper. When you hear that ‘property prices have improved’ that means, bizarrely, that they have got worse, i.e. more expensive.

Continual immigration suits the capital owning classes fine, it depresses wage costs, it provides a short-term fix and profit. Continual immigration also suits the lefty liberal faction as well, as it provides a ready source of votes, and issues they can exploit.

Now an entire younger generation faces chronic employment insecurity and accommodation insecurity issues. And what do we fob them off with? The nonsenses of identity politics and faux individualism via consumerism and social media. No wonder we also have a mental health pandemic.

We should supposedly feel grateful for all the care workers, nurses, and doctors we have imported from abroad. Surely, we should feel ashamed that we have deprived poorer countries of these people by importing cheap labour and skilled people more cheaply trained abroad, rather than properly funding such work and training here.

The UK has become absurdly overcrowded, the cities become increasingly nasty and unpleasant places to live, the countryside shrinks, and the physical and psychological environments become degraded. Nobody hitch-hikes or lets their kids outside unescorted, and nobody leaves their doors unlocked anymore.

The current course will not prove sustainable. Economy staff from abroad will increasingly demand parity, and the ecology of these isles will collapse further through sheer overcrowding. I have not seen a Puffin south of Hadrian’s Wall or Anglesey in a long while.

Vast amounts of UK capital now get invested abroad in the sweatshops of the developing world. We should force its reinvestment here to redress the chronically low productivity.

The majority of UK wealth has become either invested in property or offshore. Some might call this a Developed Economy, it looks more like a Decadent Economy.

The Decadence of the UK economy reaches a pinnacle in the financial centre of the City of London. Here the difference between assets and liabilities has become wilfully obscured, and most of the world’s serious proceeds from crime and corruption come here for discreet laundering.

Eventually the real bills will come in for all this. Decadence leads to decay and collapse.

The pandemic has revealed the weakness of UK manufacturing and our dependency on cheap imported labour.

Instead of outsourcing clothing manufacture to third world sweatshops we should develop high tech computer driven looms and garment assembly devices. Instead of exploiting imported field workers in appalling working conditions we should develop artificially intelligent harvesting machines and upgrade people’s pay and skills to use them.

Instead of short-term fixes and quick profits at any eventual cost we should apply our considerable brains to creating an ecologically, economically, and socially sustainable future for this country, and that means selectively De-Globalising it.


Anyway, enough rant for now. Herewith the last in the current series of lockdown beach-detritus creations; Ship eating Space Slugs (originally created to clear space debris from planetary systems, they devoured their creator species and now infect the whole galaxy). Here a Lithonian ship approaches a swarm of them, hoping its warp-lance will prove effective as a giant bug swat and flip them into hyperspace. I make this stuff to amuse my grandchildren obviously……….

Some further speculations on particle and quantum physics and 3-dimensional time: -

1) Imagine that time may have the same threefold dimensionality as space and that the ‘doubly unobservable*’ orthogonal time dimensions have a spatial signature.

(* We cannot even observe so called ordinary time, we merely infer its existence from memory, records, and expectations, we can perhaps infer the existence of orthogonal components to time from quantum superposition and probability in general.)

2) Imagine that the quanta of spacetime can rotate as spinors with various planes about various axes. Let us denote the spatial dimensions as x, y, x, and the temporal dimensions as a, b, c. As the universe has no preferential directions, only relative directions, then we can denote spatial spinor rotation as xy(z) and temporal spinor rotation as ab(c), where the first two letter denote the spinor plane and the bracketed letter denotes the axis.

3) If xy(z) corresponds to the ordinary chiral spin of fundamental fermions then ab(c) probably corresponds to the strong nuclear charge that some particles carry, and which can manifest in 3 ‘colours’ ab(c), ac(b), or cb(a) or their ‘anticolours’ if they spin in the opposite direction. Fundamental fermions can only carry one unit of ordinary spin and optionally one unit of nuclear charge and these undergo spatial and temporal inversion respectively because of their axes.

4) xy(a), xy(b) and xy(c) may represent electromagnetic charge. The fractional electromagnetic charges of quarks suggest that they may possess only one or two of such spins, whilst independent particles such as protons and electrons must carry all three. The spatial dimensions of x and y both lie orthogonal to all the temporal dimensions of a, b, and c. Electromagnetic charge undergoes temporal but not spatial inversion, the spatial orthogonality of the electric and magnetic vectors arising from an electromagnetic charge also seems to fit this model.

5)  ab(x), ab(y) and ab(z) may represent particle generation which seems to add only mass. If so, then particle generation undergoes spatial reversal, so either neutrinos act as Marjorama fermions and become anti-neutrinos on spatial inversion, or particles and anti-particles can have generation of either sign. Like ordinary spatial spin, generation spin does not seem perfectly conserved and can presumably interconvert with orbital angular momentum.

6) The waves of twist and anti-twist sent out from the spinor rotations of spacetime quanta may cause the spacetime curvatures of mass and electromagnetism and the very short range strong nuclear force. 

Sunday, 14 June 2020 12:03

Mid June 2020

The Plague Lockdown continues with slight relaxations. In the absence of human disturbance in this remote hideaway on the ocean shore, abstract thinking proceeds apace, so much so that the next oat cuisine innovation and beach detritus creation remain incomplete.

Alternative Physics

The ‘Crisis in Cosmology’ rumbles on with no resolution in sight between the model which measures the supposed expansion rate of the universe from supernovae luminosity and the model which measures it from anisotropies in the cosmic microwave background radiation. Jim Peebles, one of the main architects of the Lambda-CDM Big-Bang Cosmology has gone on record to say that he still considers it mostly correct, although incomplete, despite its limitations.

Those limitations do look serious. Peebles himself comments on the resemblance of the dark matter and dark energy hypotheses to the discredited Ptolemaic Epicycles idea.

Some people begin to wonder if the entire theoretical edifice may have structural faults. Yet few seem prepared to question what has become, since the 1930s, the fundamental assumption of cosmology – The Expansion Hypothesis. Ditch that by explaining cosmological redshift by another mechanism, and suddenly everything becomes clear and phlogiston free: -

Whilst awaiting confirmation or falsification of that, (343K reads and counting), speculation upon the nature of the quanta continues.

If ‘All science is either physics or stamp collecting’ (Rutherford) then The Standard Model of Particle Physics largely remains at the stamp collecting level without a coherent theory. It consists of little more than a big catalogue of ad hoc assumptions and particle types defined by a large number of parameters about whose origin we have no clues and with which we cannot calculate much, particularly about the insides of nucleons. The default Copenhagen Interpretation of quantum physics strongly implies that either the underlying reality lies forever beyond our understanding and/or that no underlying reality really exists at all.

Surely, we can do better than that.

A few hours tinkering with a bathrobe belt anchored at each end into heavy books on a glass table confirms the possibility of rotating a point in three dimensional space through 7200 to return it to its original orientation without tearing the belt or leaving a twist in it. You really need to do this ‘hands-on’ to appreciate the contra-intuitive strangeness of rotations of space itself. A continually rotating point in space would send out twists followed by un-twists in all directions in space.

This form of rotation known as SO(3) forms the basis of Milo Wolff’s ideas about The Wave Structure of the Electron

Here what we call a ‘particle’ appears as the point where an incoming ‘spherical wave’ rotates by SO(3) and then becomes an outgoing spherical wave. In this model we can consider a particle as a rotating point which creates the appearance of waves in the field of space, alternatively we can consider waves as disturbances in the field of space which come together to create the appearance of particles.

The outgoing wave appears as a time reversed form of the incoming wave.

The outgoing and incoming waves would together constitute a spherical Standing Wave in spacetime with the ‘particle’ at its centre and its ‘field(s)’ surrounding it.   

Such time reversal, the idea that phenomena can go both ways in time forms a crucial component of the Transactional Interpretation of Quantum Physics.

Such Temporal Symmetry readily explains the strange quantum phenomenon of Entanglement in which two particles once in contact can still show apparently instantaneously correlated behaviour when separated to arbitrarily large distances. In TIQM, waves pass backward in time from the particles to the point when they separated and correlate their behaviour.

In Quantum Superposition a particle can appear to occupy two (or more) mutually incompatible states at the same time, or rather it can appear to behave ‘as if’ it must have occupied incompatible states immediately before interacting and exhibiting behaviour because it doesn’t do both behaviours, just one of them chosen randomly.

A combination of Entanglement and Superposition leads to the popular idea that a particle can ‘be’ in two places at once.

Superposition implies that a particle can exist in two (or more) states at the same place, so what separates those states?

The idea of Imaginary Time may supply a possible answer. If time has the same three dimensionality as space then plainly we can only easily observe a single dimension of it, well we cannot really even observe that, we merely infer it because of the apparently linear sequences of events, we don’t usually see something do two separate things at once.

The two ‘other’ unobserved dimensions of time would constitute a plane of Pseudo-Space somehow at right angles to observed time (and space).

If spacetime does have three dimensions of time, then the waves associated with particles could also travel through imaginary time if the pseudo-space of imaginary time can undergo a similar rotation to ordinary space. The Transactional Interpretation could then model Superposition as an Entanglement across the pseudo-space of Imaginary Time.    

Moreover, a mixed rotation in a plane of one spatial dimension and one pseudo spatial dimension might explain electromagnetic charges and fields, whilst rotations purely in the plane of pseudo-space might model nuclear charge and its extremely short range spatial field effect.

Rotations in occluded dimensions in general might explain the apparently probabilistic behaviour of reality and the manifestation of the whole suite of fundamental particles.

The study of Natural Philosophy seeks to explore the cosmos by any means necessary to understand the universe. A century or two ago Natural Philosophy split in two and Science and Magic went separate ways. A fuller understanding of the universe will need to include both. The ‘occluded’ or hidden dimensions of time symmetry and the pseudo-spaces of imaginary time may provide the bridge which joins them back together.

It may take a while to explore and explicate this mathematically.


Ian Read who ran several Runic courses on Arcanorium College has asked me to ask around to see if anyone has saved them, as he no longer has copies himself. If you do have copies please get in touch with me. Pete.

The Epoch Owners Club has started to attract participants


Some Chaoist Political Thinking for the silly season.

Liberty, Equality, Fraternity!

How sweet that French revolutionary slogan sounds - yet it all ended in slaughter, dictatorship, and war. Fraternity rarely extends far without Patriotism.

Liberty and Equality contradict each other. If people have liberty they will compete as individuals and groups, and Equality will decline. Most developed economies have some redistributive mechanisms that take some power from the winners and distribute it to the losers to stabilise the system, but inequalities will always develop in any culture that permits Aspiration.

Equality of Outcome comes at the price of complete loss of Liberty.

Equality of Opportunity leads to the dominance of Meritocracy.

Thus, any mixture of Liberty and Equality will lead to some Social Friction.

Liberty and Multiculturalism do not sit comfortably together either. Left to their own devices within a society, subcultures will tend to self-segregate to preserve their own culture and to favour their own people. Most developed economies have some mechanisms to prevent subcultures becoming too insular or too dominant over others.

Multiculturalism implies restrictions upon Liberty, freedom of speech, and choice.

Acculturation, and the halfway house of Integration also imply some limitations to Liberty.

Multiculturalism and Acculturation create a great deal of Friction when a society attempts to promote both at the same time; when for example, it encourages the retention of a religion whilst discouraging all the social practices and attitudes that go with it.

Thus, cultures which import or contain other cultures can expect some Social Friction in addition to the Social Friction arising from the Liberty-Equality dichotomy.

Advocates of Equality will often attempt to conflate the two, and to brand culturalism as racism. The Champagne Socialists and the tiresome ‘Woke’ of the loony left specialise in this. Both the extreme left and the extreme right have a vested interest in worsening race relations.

Low Social Friction leads to dull and less creative societies. Moderate Social Friction leads to Creative Chaos in a society, and so does a lot of it, but that also brings a great deal of destructive Entropy as well.

Wealth acts rather like heat in thermodynamics, it only does useful work when unevenly distributed. If you force its even distribution, then you need other mechanisms to get things done. Naked force provides the mechanism of choice in all communist societies.

Asking how much inequality you want in a society seems oddly akin to asking how much crime you want in a society. The kneejerk answer of ‘none’ always implies a personal commitment to obeying all laws at all times, no matter how wrong or situation inappropriate they may seem.

The optimum level of Social Friction and Creative Chaos seems to arise when 1% of the population owns no more than 10% of the wealth, and no subculture or minority accounts for more than 1% of the population. Beyond these levels expect plenty of Entropy as well. There must come a point beyond which little will remain to unite us in diversity.

The current UK policy of trying to maintain economic growth despite low productivity by importing from other cultures cheap labour and skilled people more cheaply educated abroad does not seem indefinitely sustainable or cost effective. Neither did the British Empire, and for exactly the same reason - Entropy build-up.

A few of my favourite political notions: -

“Who controls the past controls the future. Who controls the present controls the past.”

― George Orwell, 1984.      (i.e. Retroactive Enchantment by censorship.)

“As a rough rule of thumb; everyone before 1800 was a bastard in today’s terms”

– An eminent historian of my acquaintance.

(If humans still exist in 200 years’ time, they will probably say the same about us for wrecking the planet.)

The ideal political system consists of a mixture of Monarchy, Aristocracy, and Democracy.

(The Classical Greeks worked that out long ago)

Absolute Monarchy leads to Despotism.

Absolute Aristocracy leads to Oligarchy.

Absolute Democracy leads to Mob Rule.

The unelected judiciary and the unelected civil service now provide more effective checks and balances to absolute mob-rule democracy than does the aristocracy and the monarchy in the UK.

The EU failed badly here. All the power in the EU lies with its civil service which became a gigantic faceless bureaucratic Synarchist Oligarchy that completely controls mere figurehead leaders and a puppet parliament.

All schemes for Utopia seem to end in Dystopia

The best political systems seem those in which nobody wins, and the Social Friction remains at a sufficiently high level to maintain Creative Chaos but does not become so high that a lot of Entropy occurs.

We have not had a significant body count from internal politics in Britain since the seventeenth century civil war. In that period, we lurched from absolute monarchy to ‘parliamentary’ autocracy and eventually back to a peculiar messy compromise of constitutional monarchy, influential aristocracy, and gradually increasing democracy. Arguably the resulting system maintained its extraordinary dynamism for three centuries partly by externalising its excess friction in colonial and imperial activities.

Sunday, 31 May 2020 11:59

End May 2020

Magic News.

EPOCH OWNER’S CLUB. An enthusiast has opened this new site with my blessing, and I shall participate. Membership costs nothing, except perhaps your immortal soul, although you will need to show that you do have a copy.

Pandemic Thoughts.

The British response to the pandemic bumbles on, charity and goodwill fill many of the gaps. Lockdown began rather late with only moderate levels of enforcement and compliance. However, the British people would probably not have accepted an early lockdown without evidence of a substantial death toll. Protective equipment levels and testing rates remain below demand, but we do not have directed labour and a command economy. British death rates do not look so good (so far) compared to some other countries, yet we do live on an absurdly overcrowded little island. Authoritarian cultures like China and Germany seem to have done better, but would you want to live there? Sometimes freedom costs lives. Do not blame the government, the alternatives seem far worse. ‘Scientific Advice’ does not mean that all scientists know and agree on everything – except until well after the event.

Herewith another sci-fi beach detritus creation: -

‘Scrap Metal Raid’

The Lithonians come from a heavy-element poor system and build ships with many stone and ceramic parts. Here a Lithonian Cruiser escorts a Tug on an expedition to a derelict forge world.

Ships from ground down construction block fragments plus a few vape wicks and bits and pieces from a dead electric razor. I suppose the whole thing stands as a metaphor for beachcombing. Plenty of rock, but not much metal. (I decline to use the hideously abundant plastic detritus on aesthetic grounds, although I suppose it would remove an infinitesimal fraction of it.)

Haute Cuisine.

Experimental Oat Cuisine recipe numbers 5 & 6 of 8,127 – (a large sack of oats lasts an exceptionally long lockdown). – OAT PIES!

It has proved both possible and rewarding to make pastry out of porridge oats: -

Mix porridge oats with about a fifth flour and a tenth oil (preferably olive oil), add a little water and stir and knead till it forms a thick dough like ball.

Grease up a cupcake baking tray with a little margarine or butter. Squish and roll the dough out thin on a floured board and cut out circles to form the pie cups and lids.

Savoury filling: - flaked tuna mashed up with mango and lime chutneys and hot peri sauce.

Desert filling: - dried mixed fruit and chopped glace morello cherries mingled with grated 85% cocoa chocolate. No sugar!

Bake for about 30 minutes at 1700.

The desert version tastes far better than those sickly mince pies that christmas inflicts on us annually.

Esoteric Physics News.

The previous blog did indeed ignite a spark, a specialist in Geometric Algebra got in touch.

Can we navigate through the mind-storm of bivector rotational planes, multivectors, pseudoscalars, and spinors in n-dimensional spacetime (where n remains debatable) to immanentize the prime axiom of Hermes Trismegistus - the unity of the Microcosm and the Macrocosm? In short, do the quanta of elementary particles phenomenise isomorphically to the vorticitating hypersphere of the entire universe?

BREAKING NEWS 2/6/20 : -

<But the patterns do not just show that the universe is not symmetric, but also that the asymmetry changes in different parts of the universe, and the differences exhibit a unique pattern of multipoles.

"If the universe has an axis, it is not a simple single axis like a merry-go-round," Shamir said. "It is a complex alignment of multiple axes that also have a certain drift.">

It does begin to look like the vorticitating hypersphere with Hopf fibration ‘axes’ as predicted by Hypersphere Cosmology here

Monday, 18 May 2020 19:48

Late May 2020

Magic News.

An enthusiastic correspondent has started putting together an online forum for THE EPOCH OWNERS CLUB, in which participants can discuss their work and experiences with it. I have had a look at the layout and format. It looks good and I will participate when he declares it open. Watch this space for further details.

Now Online at

Haute Cuisine.

Oat Cuisine recipe number 3 of 8,127 – (a large sack of oats lasts an exceptionally long lockdown). - Savoury Oatcakes from Porridge Oats.

Note the non-quantitative nature of the entire Oat Cuisine Range. Cooking becomes so much more intuitive and creative and fun without measurement. After a hard day’s painstakingly accurate cosmological and quantum hypersphere mechanics, sculpting and cooking by eye comes as blessed relief.

Oil up a shallow baking tray and heat an oven to about 200 C. Mix porridge oats with about a fifth flour and a dash of oil, and add anything savoury to hand, like grated cheese, herbs, pepper, seeds, spices, etc. Stir in a little water till the mixture becomes a thick paste. Spoon dollops of the paste onto the baking tray and squish them flattish. Bake for about a quarter of an hour or until agreeably brownish and crispy. Delicious and fortifying, hot or cold. 


Beach detritus fantasy creations continue with this: -

Arachnid Empire Outpost, with nest cone, spidership, and termite slave towers.

The nest cone and base consist of some sort of lightweight building composite that washes up here, and which grinds away easily against flat stones or bits of scrap metal. The termite towers consist of lengths of sea rusted iron rod. The spidership started off as a grapnel fishing weight, a covering of araldite smeared all over it provided a surface which when gone over with a thick black marker came out with an insectoid sheen.

Pandemic Thoughts.

A Shub-Nigurath - Cthulhu perspective.

Life on earth only tried high intelligence comparatively recently. For billions of years it experimented with other strategies like giant reptilian bodies, aerial flight, and hundreds of millions of species of insect. Will the high intelligence strategy pay off? The most ‘intelligent’ species that has so far evolved has already done spectacular damage to most of the rest of life on earth. The so called Anthropocene (Human created) Mass-Extinction of other species proceeds at a terrifying pace, we have ripped up the earth and polluted the land, the skies, and the seas, and our numbers seem set to grow by billions more who will want gigatons more of everything.

Covid 19 looks like the biosphere taking a swipe at a rogue species, not a particularly vicious swipe because it probably won’t kill more than a mere one percent of us, but it could do much worse next time.

High intelligence seems a risky strategy for life on earth to pursue. In the long term it will only pay off if the high intelligence species manages to plant life from earth in other star systems. Otherwise life on earth will probably have shortened its own life expectancy by trying this experiment, unless the ‘intelligent’ species becomes truly intelligent.

Octachoron and Hypersphere.

Some Azathothian musings…….

Herewith a 3-dimensional representation of a 4-dimensional hypercube.



(Scrap wire and superglue, the araldite having run low, the whole perched on a spare pyramid,)

A hypercube can assist with the visualisation of the geometry and topology and rotation of a hypersphere in both cosmological and quantum contexts.

The hypercube consists of a four-dimensional cube, and it has many possible perspective representations in the 3 spatial dimensions that we can perceive.

Some preliminary thoughts on the applicability of hypersphere mechanics to cosmology and particle physics now follow: -

The 4-dimensional hypercube, sometimes also known as a tesseract, also has the mathematical name of an Octachoron as it has eight cubic cells. The eight cubic cells appear in the above model as the more obvious inner and outer cubes and the less obvious six truncated pyramids that join the inner to the outer cubes. In this 3-dimensional representation these six cubes become distorted by perspective into truncated pyramids. In a real four-dimensional cube, all eight cubes have the same size, so perspective has also made the ‘outer’ cube appear much larger than the ‘inner’ cube.

The Octachoron has the usual x, y, and z axes of a cube and of 3-dimensional space, and its fourth spatial axis w corresponds to the ‘diagonals’ joining the ‘inner’ and ‘outer’ cubes. In a hypersphere the fourth spatial dimension w will appear to 3-dimensional observers as a curvature or an acceleration.

This makes the Octachoron a useful visualisation tool when considering the dynamic behaviour of a hypersphere which we usually represent in three dimensions as either a point surrounded by a spherical surface representing the antipode of that point, or as two spheres of equal size with every point on the surface of each sphere in contact with a corresponding point on the other, (imagine them rolling all around each other) and the centres of each sphere representing the observer and the observer’s antipode.

In the Octachoron each of the six truncated pyramids lies antipodal to the one opposite to it across the ‘inner’ cube. Strange as it may seem, the ‘inner’ cube lies antipodal to the ‘outer’ cube, analogous to the way in which the ‘central’ point of a hypersphere projected into 3 dimensions has its antipode point spread out into a spherical surface around it.

Visualising the rotations of a hypersphere remains exceptionally difficult as it has no obvious planes or edges to act as reference points. However, the Octachoron does provide a model of four-dimensional closed space which also comes with built-in three-dimensional Cartesian axes x, y, and z, corresponding to the edges of the undistorted ‘inner and ‘outer’ cubic cells.  

As these videos show, rotating an Octachoron through a plane of one of the x or y or z directions and the fourth-dimension w, turns it inside out and back again: -


The following diagram shows a side view of an Octachoron undergoing an 1800 rotation about a wx plane from one end of the diagram to the other. Note than in addition to turning the figure inside out, the rotation also turns each cell into its mirror image.

Using the quaternion algebra of rotations, we can equate an 1800 rotation with i2 as it inverts the figure (i2 = -1).

Thus, by Hamilton’s formula i2 = j2 = k2 = ijk = -1

if we equate i, j, and k with a 900 rotation about the wx, wy, and wz planes then a 900 rotation simultaneously about each will completely invert the Octachoron or Hypersphere and turn it ‘inside out’ and into its mirror image, a further 900 rotation of this kind will restore the original configuration. Note that each rotation can have two possible directions designated + and -, or r and l. Such rotations about three planes simultaneously only work as above if they all have the same direction.

An Octachoron rotating in the -i-j-k mode would effectively act as an Anti-Octachoron to an Octachoron rotating in the +i+j+k mode. This may underlie the manifestation of fermion quanta as either particle or anti-particle.

This triple rotation involving the w axis would appear in three-dimensional space as a spherical wave traveling either inwards or outwards depending on its sign. It may explain the origin of gravitational and electromagnetic and perhaps nuclear fields. On the cosmological scale it provides a model for the hyperspherical vorticitation, the special kind of rotation which prevents the cosmic hypersphere from collapsing under its own gravity.

Now all fundamental particles have a measurable Spin corresponding approximately to rotations in three dimensions by rotation about a single xy, xz, or zy plane. The somewhat peculiar nature of this Spin may arise from its origin as an isoclinic double plane spin such as xy/wz.

In addition to Spin, fundamental particles can also have one or more of two properties which can come in THREE possible ‘strengths’ viz-

Electromagnetic charges of 1/3, or 2/2, or 1 (or their negatives)

Particle Generation (charges?) of 1, 2, or 3 (or their negatives)

Plus, fundamental particles can in principle have one of three possible Nuclear Charges (designated red, blue, and green (or their anti-colours)) although only composite particles exhibiting all three or a charge - anti-charge configuration have any kind of stability.

Now if time has three dimensions rather than just one as commonly assumed, and all three lie mutually orthogonal (at right angles) to each other (as with space), then the two time dimensions orthogonal to the direction of observation used by an observer constitute an imaginary time plane corresponding to probability lying at right angles to time. Imaginary time would constitute a sort of ‘Pseudo-Space’ by the Minkowski formalism that counts time as an imaginary space.

As the two axes of pseudo-space, which we can designate u and v, must also lie mutually orthogonal to all the spatial dimensions x, y, and z, a number of further rotational possibilities and degrees of freedom become possible, viz-     

ux  uy uz        vx  vy vz        wu  wy  wz

Between them these ‘exotic’ spins may somehow account for the electromagnetic, nuclear, and generational charges of fundamental particles.

Work continues………… I put this out there to see if it ignites any sparks.

Thursday, 30 April 2020 16:10

May 2020

Something extraordinary came out of the bubonic plague of 1665-6. Isaac Newton retreated to the family farm and developed the equations of gravitation. Hopefully, this current lockdown may lead to some interesting innovations.

With a provisionally credible and currently unfalsified model of the Yog-Sothian hyperspherical geometry of the cosmos awaiting confirmation: -

Thought returns to the microcosm of the quanta, the realm of the blind mad god Azathoth.

At present we have  a model encompassing a considerable number of types of quanta each of which may have its own type of field and each of which can behave as both a point particle and as an extended wave and which can apparently exist in several contradictory states at once and which can apparently have instantaneous connections at any distances. We have mathematical recipes for some of these phenomena, but the maths involves un-visualisable concepts and abstract dimensionalities and some of the phenomena remain apparently completely random.

How in hell does the tiny stuff apparently underlying the whole of reality really work?

The following musings consist of hand-waving arguments, intuitions, guesses, and speculations, the supporting maths may follow later.

Firstly, Fields. According to quantum field theory, every quantum consists of an excitation of a quantum field that extends throughout all of space. This implies that maybe four or perhaps twenty-four different kinds of fields pervade all of space. Do the quanta subtend these fields around themselves or should we regard the fields as more fundamental and the quanta as mere disturbances in them? If, as in General Relativity, mass-energy tells space-time how to curve, and space-time tells mass-energy how to move, then they both represent aspects of the same phenomena. Any particle of mass appears as a curvature that extends throughout all of space, it merely appears to have a solid boundary around it because of short range electrostatic effects. So perhaps quanta and fields represent aspects of the same phenomena and we should regard neither as separate nor more fundamental.

Gravitational waves and electromagnetic waves always appear to propagate at the speed of light, in accordance with the idea that such waves represent moving disturbances in such fields originating in the accelerations of objects carrying mass or electric charge. However static masses and electric charges give every appearance of exerting instantaneous effects over any distance although the forces do decline by the inverse square of distance where Euclidian geometry applies. Arguments over whether static fields exert instantaneous or lightspeed effect continue but seemingly instantaneous effects do appear in the non-local models of some interpretations of quantum mechanics.

Thus, the daunting Particle-Wave Duality of most interpretations of quantum physics perhaps needs extending to an even more daunting Particle-Wave-Field Triality before we can make any real sense of it.

The Field component of reality probably does not need four or twenty-four components, it probably consists of a single Field with a somewhat greater than 3-space, 1-time dimensionality. A Field with a symmetrical 3-space, 3-time dimensionality with both 3d space and 3d time curved to form a hypersphere might do the trick. A 3s3t spacetime metric appears to offer just exactly enough degrees of freedom to account for the manifestation of all the quanta observed so far. (It predicts an additional Duon boson only, and it denies that the Higgs mechanism applies to this universe and that we have really detected a Higgs boson.)

See for some preliminary speculations.

In addition to having probability lying at right angles to ‘ordinary’ time in an orthogonal plane of imaginary time (in an observer’s frame of reference) we probably need to accept the two-way nature of time that most of the physics and some of the magic suggests. This does not seem restricted to the realm of the ultra-small as the following example illustrates: -

We can easily observe back-reflection when looking at a widow with low light or darkness behind the window. We can see a reflection of ourselves and our surroundings in the window as some of the light hitting it reflects off the front surface of the glass, whilst some of it goes through the glass (as others can see us from the other side of it). Now the amount of light which becomes reflected back off the front surface depends on the thickness of the glass!

This seems deeply weird. How do light quanta anticipate the thickness of the glass before deciding whether to bounce off it or to go through it? The Transactional Interpretation of Quantum Physics seems to offer an explanation. In this interpretation, the forward wave function of each quantum of light goes through the glass and it also reflects off the glass as well in search of an electron in someone’s eyeball or in the scenery to act as a receiver. Potential receiving electrons send a confirmation wave BACKWARDS IN TIME down the wave path to the electron which emitted the light quantum in the first place. The thicker the glass the more trouble the forward and backwards waves have, so a handshake between forward and backward waves along the air only reflection path becomes more likely. The handshake results in the collapse of the completed wave function and the effective exchange of a ‘particle’ of energy between emitting and receiving electrons. The wave functions act like a mysterious type of aether which acts across time to feel out possible futures.

From some perspectives the light quantum or photon exists only as a wave/anti-wave exchanged between electrons, but what about the electrons themselves and everything else we think of as ‘matter-particles’? Matter quanta also exhibit wavelike qualities too, and perhaps in a six dimensional vorticitating hyperspherical universe they may consist of overlapping wave/anti-waves that go right round the universe with the endpoints representing particles and the antiparticles they may rotate into at their antipode points.

I have a few thoughts on this which I have not fully explicated or incorporated into hypersphere cosmology yet, but it goes a bit like this: -

In Cramer's Transactional Interpretation of Quantum Physics, we can view a 'photon' as an exchange of retarded and advanced waves between electrons.

In some senses we can consider photons as the endpoints of standing waves. 

'Matter' particles also have wavelike properties as de Broglie showed.

Milo Wolff takes this a step further with his Wave Structure of Matter and has matter particles as the points where inward and outward standing waves converge, but he has the inward waves reflected from the entire universe.

In Hypersphere Cosmology every point in the universe has an antipode point.

Thus every 'matter particle' may consist of the endpoint of a standing wave that goes right round the universe with an 'anti-matter particle' at the other end of it.

Thus, the universe could have an overall matter-antimatter balance with the two kept well out of each other's way.

Perhaps we should regard The Field, in which quanta exist as wavelike or particle-like excitations or which quanta subtend around themselves, not as something which fills spacetime but as spacetime itself.


Lockdown has achieved some remarkable results: - Reduced fossil fuel use and carbon emissions, zero economic growth, wildlife thriving, men growing their hair back to a proper hippy length, fewer people buying pointless stuff and junk, everybody devising new forms of self-entertainment and looking out for their friends and relatives, the professional classes home educating their offspring better than schools, people having time to reflect on who and what really matters to them in this life.

Perhaps after this pandemic finally ends, we should institute some form of annual three-month public holiday every year.

Historically we have tended to favour oats for high performance creatures like racehorses, gladiators, and highlanders. It seems a good move to base most of one’s carbohydrate intake upon the proteinaceous and roughage rich foods of oat porridge and oatcakes.

So, herewith in response to the overwhelming acclaim for savoury Tuna-Porridge in the previous blog, a sweet dish to complement it: -

Oat Cuisine Recipe Number 2 of 8,127, (a large sack of oats lasts a long lockdown). Place a cupful of oats in a saucepan, add dried mixed fruit, glace cherries, any nuts or bits of fruit available, a teaspoonful of powdered ginger and/or mixed spice, a splash of dark rum and a little water. Warm with stirring until it forms a thick paste. The nutritious result usually tastes like a delicious hot fruit-cake puree.

Another beach detritus sci-fi spacehulk: - The Orbital Space Monitor ‘Misanthropy’.

The Misanthropy has a bad attitude. It fires upon anything that approaches the abandoned star system it has guarded for several millennia - a sort of metaphor for social isolation.

The base consist of the end of a charred aluminium drinks can recovered from a beach fire pit. The spacehulk’s body consists of a rare sea worn volcanic bolide of iron rich vesicated basalt. A few drops of Araldite hold it all together.    

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