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Published: 12 October 2025

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Octblog 2025

Hagiography

My thanks to Marcus Hedare for this thorough and highly comprehensive introduction to my magical ideas: -

https://vocal.media/bookclub/peter-j-carroll-architect-of-chaos-magic

Infinities in Cosmos and Quanta?

Our species currently seems either to have encountered two limits to what it can in principle know, or it has manufactured them by its choices of epistemology.

One limit concerns Black Holes where the equations of General Relativity break down and tell us nothing about what occurs inside of them except perhaps to expect the formation of spacetime singularities of infinite density without any space or time at all and about which we can know nothing. This limit exactly reflects the limit to knowledge that the Big Bang theory imposes. A naïve extrapolation of General Relativity coupled with the questionable assumption of  the hypothesis of an expanding universe leads back to a zero sized initial singularity point for the universe about which we can know nothing. We cannot, even in principle, know how it came into existence and even if anything came before it.

Another apparently unsurmountable limit to what we can know arises down at the other end of the scale with the Quanta. Both the  Schrödinger Wave Equation and the Heisenberg Uncertainty Principle assume that fundamental quanta exist as point particles of zero size. The  Schrödinger equation describes where such point particles may appear as they move, but only in in terms of probabilities,. The Heisenberg uncertainty principle describes such point particles as having either indefinite position or indefinite momentum, and either indefinite energy or indefinite duration. The probabilistic and partially indeterminate descriptions of point particles rule out, in principle, any possibility of knowing anything more fundamental about them.

The calculations we can perform using the epistemological assumptions of spacetime singularities or point particles always yields meaningless infinities, as division by zero always does.

In conventional cosmology we simply have to ignore the question of what might go on inside black holes and in conventional quantum field theory we simply have to ‘renormalise’ the theoretical infinities away and substitute actual measured values.

Unsurprisingly, the attempt to meld these epistemologies together to create a theory of Quantum Gravity that resolves the flaws in both, has not yielded useful results.

Hypersphere Cosmology at least eliminates spacetime singularities and a big bang from a description of the cosmos at the small price of positing a curvature dimension to the universe, and it currently remains unfalsified by observations. It sets a limit to how small anything can become.

Perhaps our quantum epistemology requires an analogous limit of non-infinite smallness, and some form of extension if only in dimensions not currently acknowledged. Work continues……..

Shub-Nigurathian Apocalypse Immanent?

Imagination has already created the infrastructure for an Azathothian Apocalypse. We currently have currently stockpiled about 10,000 nuclear warheads replete with delivery systems, to err, keep the peace.

Many warn about a possible Cthulhu Apocalypse if we let Artificial Intelligence enhance our collective stupidity.

Apart from a few sci-fi writers, few have considered the apocalyptic potential of what will soon become possible with our biology. We just passed what we may come to recognise as a milestone by achieving Mitomeiosis – you may wish to google that. Something whispered in my psyche a long while ago that Physical Immortality lays only a few steps beyond that, and all hell will break loose when we achieve it.

Xi Jinping and Vladimir Putin apparently discussed immortality the last time they met in person. Hopefully neither will live until it becomes a reality.   

 Dean Radin’s New Book

https://www.deanradin.com/

Herewith my requested comment for it: -

Dean Radin’s book certainly provides a wealth of material and inspiration for practical experimentation and the advance of magical and scientific theory. I recommend this ideas-rich and entertainingly written Science of Magic to every open-minded scientist and to every serious magician on the planet. - Peter J Carroll, physicist and sorcerer, Past Grandmaster Illuminates of Thanateros.

Multimind

Lastly a brief article from a scientist and polymath who makes a preliminary stab at identifying the brain structures underlying some of the functions of our inner pantheon in our manifestly non-singular minds. Nice fun graphics.

https://www.researchgate.net/publication/396267955_NUGAE_-A_PANDEMONIUM_MODEL_OF_MORAL_CHOICES

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Published: 10 September 2025

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Septblog 2025

Flat Universe Theory ?  I got so irritated by reading repeated assertions that we know that we inhabit a flat or vanishingly close to flat universe that I delved into the observations, assumptions, and interpretations that purportedly support this. It turns out that the proponents of the ‘standard’ or ‘concordance’ LCDM Big Bang expanding universe model have nothing better to offer than a forced match between the apparent size of temperature variant spots (about 1 degree) in the CMBR and their assumed distances from the observer, making Euclidian triangles. Equations 16 and 17 of Hypersphere Cosmology clearly reveal the fallacy of this approach.

See the following addition of this for further explication and emphasis: -

 https://specularium.org/hypersphere-cosmology-articles/flat-universe-theory-dies

The Holographic Principle often gets a mention in Cosmology, but I think convention has it the wrong way around. This universe does not seem like an information projection from its 2D surface boundary into an apparent 3D space, but rather it seems more realistically like the stereographic projection of the 3D surface of a Hypersphere into an apparent 3D sphere surrounding any observer.

Otroversion.  I don’t often find a book on psychology that speaks convincingly to me.

The mind (the most complicated structure in the universe known to us) has an amusing tendency to provide superficial confirmation of almost any psychological map or model that we try to impose upon it. Thus Astrology, The theory of Humours, Kabala, Jungianism, Freudianism, Behaviourism, and the Five Factors Model, have a way of seeming persuasively explanatory but lacking in predictive power.

A new book – ‘The Gift of Not Belonging’ by Dr Rami Kaminski identifies a personality trait that seems previously uncategorized except perhaps vaguely as ‘outsider’.

Kaminski explores in depth the Otrovert personality which rejects social convention and received wisdom instinctively, doesn’t like communalism and groupthink about anything, prefers a few close friends to belonging to a herd, works far better as an individualist (or leader) than a team player, and craves personal autonomy above all else. Whilst Otroverts can do extroversion they don’t feel comfortable with it. Kaminski identifies Otroverts as a definite Type that society does little to encourage, although it often eventually values what they create. Perhaps we should view it rather as a Trait that some people exhibit to a high degree. I found myselves scoring very high on most but not all of the characteristics of Otroversion. I could not help noticing that Otroversion seems a very pronounced trait amongst Magicians who seem a particularly ornery, antinomian, and querulous bunch. If Uranian Octarine has a characteristic personality trait it must come close to the Otroversion that Kaminski identifies.

 https://www.amazon.co.uk/Gift-Not-Belonging-Outsiders-Joiners/dp/1917189222

Amanita Highlands.

The Scottish wing of my clan lives in the highlands surrounded by groves of Downy Birch which in the autumn sunny breezes flutter languidly almost as if underwater, admitting dappled sunlight to the lush mossy undergrowth where all manner of strange fungi sprout, some standing alone and looking strangely alien against the green underfoot, and some clustered in mysterious looking miniature cities. The star of the show always remains for me the Fly Agaric: -

Nobody has a convincing idea about why mushrooms and toadstools have the colours they do, the colours do not seem to correlate with their edibility or toxicity to any other species in a systematic way, nor to any sort of camouflage or advertising strategy.

Decades ago on the Isle of Arran I made a startlingly orange milkshake out of an Amanita about twice that size and drank the lot to no effect, but they do apparently vary considerably in their alkaloid content, and can prove dangerous.

Autumn in the highlands comes late, it all seems still very green here, and purple where the heather flowers on the mountainsides, best of all the midges have largely gone, and the bakeries have steak pies, without a ghastly west country gristle & veg pasty in sight.

The Politics of REFORM.

The UK has taken the easy way out for decades.

It has used immigration to depress wages and training costs and to inflate property prices in lieu of achieving any real growth. This has become a vicious circle which has forced down the birth rate of the indigenous population and eroded social cohesion. Our cities have become prohibitively expensive to live in and bad places to bring children up in.

It has handed out benefits for votes right across the political spectrum. 25% of Pensioners now qualify as millionaires. We now effectively have a Universal Basic Income – just sign on as unemployed and then get a mental health qualification (more or less available upon request) and you can claim enhanced benefits indefinitely.

Our population grows but the economy does not, and the effective workforce shrinks.

Sorting out these two huge problems will entail taking some radical, brutal, and widely and wildly unpopular actions.

Does it necessarily entail abandoning Green Policies? The Reform Party seems to think so, and the Conservatives and Labour seem tempted to follow.

If we burn up all the fossils fuels we can, and tear up all the remaining countryside and farmland we may create a short term boost to the economy but it will not solve the twin crises of immigration and indolence.

Britain’s relatively small contribution to total global warming and environmental destruction should not provide an excuse to continue making it. Rather we should seek to become the world’s leading green economy and to export the expertise and technology that goes with it.

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Published: 16 August 2025

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Augblog 2025

Augblog comes a little late due to a number of summer clan gatherings, plus a certain preoccupation with game design, and some extended conversations with various usually pseudonymous physicists about Hypersphere Cosmology (presumably such people wish to avoid peer disapproval of their interest in such heretical interpretations of the data) but don’t worry -  the Physics Department and the Magic Department of Arcanorium College treat all enquiries in the strictest confidence. Your unpublished reservations about orthodox theories, and your speculations, hypotheses, and identities remain safe with us.

Doubly Modified Newtonian Dynamics? (DMOND)

The debate about whether Dark Matter or Some Kind of Modified Newtonian (or Relativistic) Dynamics best explains the apparently anomalous rotational behaviour of galaxies and their varied shapes and sizes rages with increasing intensity.

Galaxies present as extremely diverse structures – some look huge, some look smaller, most but not all seem to have central black holes, they all seem to rotate but often in ways that violate Newtonian or Relativistic expectations based on our estimates of the amount of ordinary (Baryonic) matter that they contain. Galaxies contain visible baryonic matter in the form of incandescent stars and less easily detectable baryonic matter in the form of rocks and dust and gas – which almost certainly includes very extensive spherical gas halos that extend very far beyond the incandescent stars, as definitely seems the case for the galaxies nearest to ours.

Whether or not galaxies also contain some sort of non-baryonic Dark Matter that accounts for their anomalous rotational behaviour and their morphology by just supplying more invisible mass and hence more gravity but otherwise not interacting much at all, remains contentious. If they do, then such Dark Matter would need to occur in varied amounts and in rather improbable configurations to resolve the rotational anomalies. Moreover, many galaxies would have to contain about five times as much of this mysterious and otherwise undetectable substance as the ordinary (Baryonic) matter made of protons, neutrons, and electrons that we know of.

Alternatively, we can try and make sense of galactic rotations by adjusting our theories about the effects of gravitation and inertia at the vast scales of entire galaxies.

Basic MOdified Newtonian Dynamics (MOND) depends on simply adding an extra acceleration a_o to the cosmos to account for the apparently missing gravity. Although the origin of a₀ remains unexplained, it does at least model the behaviour of some galaxies well, but not others – and thus, many cosmologists continue to prefer to use equally ad hoc arrangements of ‘whatever hypothetical configurations of dark matter it takes’ to resolve the anomalies.

Hypersphere Cosmology models the cosmos and its galaxies using Doubly Modified Newtonian Dynamics (DMOND) in which both gravitation and inertia become modified with effects that show up easily only on galactic scales.

Equation 9) shows how the rotational velocity v, at the radius (r) of a galaxy depends on the  velocity v_i(r) from Newtonian theory, plus an additional velocity of 2(sqrt pi G d)r from a Gödelian rotational component of the entire mass of the galaxy right out to the limit r of the vast spherical gas halo which seems likely to surround every galaxy.

Equation 10) shows how Newton’s Second Law, F = ma, remains subject to modification by the small positive curvature of the entire hyperspherical universe which gives rise to an omnidirectional deceleration A, where GM/L² = A. Note that this mechanism does not violate conservation of energy as it converts linear momentum into orbital momentum.

I suspect that a combination of both of these effects together with fuller datasets on galactic gas halos can explain the apparently anomalous galactic rotation curves without recourse to the hypothesis of Dark Matter or any other form of Phlogiston.

All criticism and collaboration welcome.  

That Space Game. The obsession/distraction that keeps on giving has now become more easily portable between main and holiday homes with the innovation of a modular board of moveable hexagonal tiles. Nevertheless the full set of all metal starships (nuts and bolts, ball bearings and various carpentry and plumbing fittings) and the board tiles  still weighs in at over 10kg.

Developments continue and possibly converge towards a final form. I decided to throw all my favourite game concepts into this.

The provisionally re-titled Spaceforge War has the following new experimental features:

1) Hexagonal tiles - plywood coaster blanks sprayed matt black and then marked to show star systems within ~20 light years of the solar system, 5 lightyears to a hex.

(Alternatively the reverse sides of the Hexes can represent abstract or sci-fi fantasy arrangements of star systems.) (Shades of Twilight Imperium but the pieces do fit the board and it remains playable in a single day.)

2) The basic rule structure depends on sequential moves and dice to settle search and evasion and combat between units. (Rather like Risk protocols but with polyhedral dice.)

3) The tournament rule structure depends on simultaneously revealed movement orders (as in Diplomacy) and the use of simultaneously revealed tactics of search and evasion and combat, resolved by reference by asymmetric polygons.

4) It has endless scope for the introduction of Alien Mercenaries or Invaders, Ground Forces, and Characters or Psi-Devices which modify production, movement, search/evasion and combat etc.

If satisfying playable self-consistent rule systems emerge from all this, they will appear in the Games sections in due course. Work continues.

Weakening Dark Energy?

A flurry of papers and articles has appeared this last year in response to astronomical observations which suggest that something looks very wrong with mainstream ideas about so called ‘dark energy’ . It appears that this piece of phlogiston will require yet another aliquot of phlogiston to patch it. Some theorists have started to reexamine Gödelian rotating universe ideas: -

https://www.space.com/astronomy/a-spinning-universe-could-crack-the-mysteries-of-dark-energy-and-our-place-in-the-multiverse

https://arxiv.org/html/1910.10819v2

Yet they try to patch the problem whilst still adhering to the Expansion Hypothesis.

A rotation of a non-expanding hyperspherical universe (in which bodies vorticitate around randomly orientated Hopf Fibrations) can solve the problem, but not in the way they think. The hypersphere model has balanced centrifugal and centripetal accelerations/curvatures of c²/L. This results in cosmological redshift and in us observing the universe in Stereographic Projection which creates the optical illusion of accelerating cosmic expansion.

At all points in 4D space and time the universe remains: -

4 Gigaparsecs to Antipode, and vorticitating  at 0.005 arcseconds per century in finite and unbounded spacetime.

A more satisfactory metaphysic methinks.

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Published: 01 July 2025

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Julblog 2025.

Three Dimensional Time!

https://www.worldscientific.com/doi/10.1142/S2424942425500045?srsltid=AfmBOoq3OjMeq9TFUl3bG6YiBNnw93_layQkfNe4qzVnyddLdr_ukJZh

At last, this seemingly crazy and somewhat occult idea that I’ve speculated upon for decades has started to attract the serious attention of mainstream physicists.

If this hypothesis thesis pans out, it has massive scope and implications for physics, metaphysics and magic.

Garden Statuary – Pan in celebration of Midsummer.

Many hours work with the Turdcrete or Hypertufa has led to the completion of the figure whose wire frame appears on the previous blog. You have to apply the stuff a little at a time and let it at least partially set, or it sags. Black liquid mortar dye in the material supplies the base colour which then gets a dry brushing with green acrylic to create a faux weathered bronze effect. A matched pair of 20 Carat Pear Cut Burmese Rubies for eyes contrasts with the verdigrised surface, or a couple of red glass ones prized from some Indian style costume jewellery earrings will also serve.

Reality from the bottom up.

A man needs a hobby to distract himself from the relentless pursuit of sculpture, so herewith some further thoughts upon the Quanta underlying reality, which may have esoteric implications.

Hypertorus Quantology?

How does reality work?

The Hypersphere Cosmology thesis which remains unfalsified at the time of writing, attempts to describe how it works on the cosmological scale with observational evidence that we can interpret in its favour still coming in.

But what about reality on the fundamental subatomic scale?

Which interpretation of quantum physics do you prefer?

Most interpretations attempt to describe what goes on in the quantum realm in terms of something that we can represent with images and words.

Yet the orthodox ‘Copenhagen’ interpretation asserts that we currently have no way of choosing between any of the interpretations of the ad-hoc and highly abstract mathematics which can accurately predict the probabilities of obtaining some particular measurements. The Copenhagenists insist that we can know nothing about the unobserved states of quanta between measurements, and we cannot, and should not, attribute any kind of reality or word or image description to them. We should merely ‘shut up and calculate’ because the stuff of the world doesn’t seem to behave like macroscopic stuff at all on the quantum level. Thus, we can only make abstract mathematical epistemologies to describe and predict our observations because quanta do not consistently behave like waves or particles or any other macroscopic phenomena that we can imagine.

This does seem an incomplete, unimaginative, and metaphysically unsatisfactory position that becomes more annoying  with every reiteration of it.

The Geometric description of reality on the cosmological and macroscale as implied by General Relativity,  "Matter tells spacetime how to curve, and curved spacetime tells matter how to move",  has proved highly effective in modelling much of the structure and behaviour of the cosmos. (Hypersphere Cosmology builds upon this with added modifications to avoid spacetime singularities.) Surely this behoves us to consider geometric models for the quanta of matter and energy as well.

The standard models of cosmology and quantum physics both share a common problem – the mathematical spacetime singularities they imply inside of black holes and at a big bang, and those that arise from treating quanta as point particles.

Any geometric description of quanta would need to model their spins, electric and nuclear charges, and ‘flavours’  for starters, and also account for quantum entanglement.

Any geometric model of reality presupposes that spacetime itself must have some sort of geometry to it. In such models, ‘space’ does not have the merely privative quality of representing the absence of matter between items of matter, nor does ‘time’ have the merely privative quality of representing the absence of events between events. Rather, in a geometric model, spacetime must consist of some sort of structure, subtended perhaps by the presence and action of matter and energy – or perhaps equivalently we can regard matter and energy as twists or knots or some other form of geometric distortion of the fabric of spacetime.

Assuming that spacetime does consist of something, and leaving aside for a while the question of what that something might consist of, what sort of geometric features in it could account for the behaviour of the quanta of matter and energy – the fermions and bosons - that seem to underlie all of the stuff of reality?

The Torus shape has some intriguing geometric properties.

See https://en.wikipedia.org/wiki/Torus

(Note within also the four dimensional torus or Clifford Torus, the simplest Hypertorus.)

Herewith follows the beginnings of a qualitative handwaving argument, the math may eventually follow……..

A torus can in principle rotate about itself in two different ways without changing its orientation in space. A toroidal rotation simply spins it in the plane of the major circle of a (ring) torus. A poloidal rotation consists of a rotation in the plane of the minor circle of a (ring) torus. (Imagine a circular rod spinning around along its long axis and then imagine twisting the rod around into a circle.)

Why should it rotate? Well the Gödelian principle that ‘Matter everywhere rotates relative to the compass of inertia with an angular velocity of twice the square root of pi times the gravitational constant times the density’, W = sqrt(piGd), presumably applies at all scales. Hyperspheres and tori both have the same volume formulae 2pi²r³.

A smoke ring consists of a poloidally rotating ring of air with smoke in it that makes it visible. So-called vortex cannons can launch invisible ones without smoke in them, but they both dissipate over distance due to collision with air molecules.

Consider the simplest fermion or quantum of matter, the Neutrino, a blizzard of which (mainly from the sun) continually passes right through our bodies and our planet to almost zero effect. Neutrinos come in two basic forms, one with a left handed spin in its direction of propagation, and the other which we call an Antineutrino, with a right handed spin in its direction of propagation, (they both propagate at or very close to lightspeed).

Now if we assume that spacetime itself can become twisted into miniature torus like vortices, then such toruses rotating in both poloidal and toroidal mode can model neutrinos and explain some of their characteristics.

In particular: -

1) The poloidal spin will result in Neutrinos constantly moving with respect to the spacetime fabric, like all quanta they can never stand still, they always move, if only in vibrational or orbital motion with each other.

2) The toroidal spin can only rotate left or right with respect to the poloidal spin, giving rise to Neutrinos and Antineutrinos respectively. This makes them antiparticles of each other which could mutually annihilate to form a photon.

3) A toroidal spin at half the rate of the poloidal spin can account for the phenomena of spin plus or minus one half characteristic of all fundamental fermions which means they have to rotate through 720 rather than 360 degrees  to regain their original orientations.

4) When fundamental quanta interact, neutrinos only deliver energy in the form of momentum and spin or carry energy away in the form of momentum and spin, both of which we can account for in terms of their two spin modes. In this model, bosons appear as particle-antiparticle pairs using the Feynman insight that we can regard antiparticles as particles traveling backwards in time and the Transactional Interpretation of quantum handshakes between retarded (forward) and advanced (backward) waves in spacetime.  

 Any form of distortion in spacetime will cause a curvature in proportion to the energy invested in it, resulting in the phenomena of mass (or momentum) and gravity for all quanta, but other quanta have additional qualities like electromagnetic and nuclear charges. If these properties also depend on spins, then such spins will have to occur in more dimensions than the usually acknowledged three of space and one of time.

The Clifford Torus, the simplest Hypertorus, consist of a 4D torus: -

https://en.wikipedia.org/wiki/Clifford_torus

We can imagine this as created by rotating a circle in a two dimensional plane around another circle in another two dimensional plane, making a four dimensional figure.

Such a hypertorus has some intriguing properties

As ‘half’ of a hypersphere, it can inhabit a 4-Manifold such as that presented in Hypersphere Cosmology for the universe.

Stereographically it projects to a torus in 3D, rather as the Hypersphere universe stereographically projects to a seemingly infinite sphere in 3D.

As with a hypersphere, its ‘inside’ and ‘outside’ become interchangeable.

Some of the rotations of the hypertorus appear stereographically projected as an inside/outside flip that passes through theoretical infinity in 3D. Mass extends to theoretical infinity decreasing by the inverse square of distance from a centre where it does not have infinite value, as quanta do not really exist as infinitely small point particles.

Musings continue. Collaboration welcome. Higher dimensional geometry, despite the visualisation difficulties, seems to offer a better route to a quantum ontology, or at least a better quantum epistemology than entirely abstract algebra.

From the Skaron Space-Yards.

Both fleets of starships, composed of beach detritus and metal scraps, undergo a gradual transformation towards a more 3D look as part of Operation Second Childhood when the surf isn’t good down at our retreat in Wales.