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 epochownersclub.freeforums.net

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. 

Craftwork.

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: -

VIDEO https://www.youtube.com/watch?v=q5Qh2XpoCsY

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.

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: -

https://www.specularium.org/hypersphere-cosmology

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 https://www.specularium.org/3d-time 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.    

Magic works in Practise but not in Theory.

I vaguely remember making this statement to Gordon White during a rather peculiar interview. We had found a large table in an empty waterfront pub and set up a microphone and recording apparatus. During the course of the prolonged interview the pub filled up with besuited office types and even the table we occupied became crowded with rather bemused clerical and administrative workers taking frequent sidelong glances at us and pretending not to listen as we ploughed on with the strange metaphysics and barely believable biography. As the general hubbub around us rose we had to speak louder and louder.

The quote keeps getting fed back to me by correspondents and it deserves further analysis; the principle seems to crop up everywhere you look.

Newton’s formulae for Gravity work well in Practise, allowing us to calculate planetary orbits, spacecraft trajectories, and the behaviour of cannonballs and falling apples. However, the Theory that the formulae imply doesn’t really make sense as it means instantaneous force at ANY distance. Neither Newton nor anyone else really liked this. The later addition of the idea of a ‘gravitational field’ doesn’t really make the problem go away. Einstein’s new General Relativistic description of gravity as spacetime curvature dispensed with forces and gave even more accurate Practical astronomical predictions, but it also leads to the unresolved Theoretical catastrophe of spacetime singularities. Work continues, hypersphere cosmology might do it.

https://www.specularium.org/hypersphere-cosmology

Quantum physics presents another example. The formulae of quantum mechanics give outstanding Practical results, allowing us to build electronic devices and lasers, however, despite the efficacy of the pragmatically derived formulae, humanity does not have a coherent and generally agreed Theory of how quanta do their stuff. Many consider that quantum field theory has only epistemological value, it describes merely our limited knowledge about quanta; it doesn’t, or cannot in its current form, describe them directly. Work and controversy continue.

Religion provides perhaps the most spectacular example of something that works in Practise but not in Theory. Billions of people find the Practise of their religion perfectly satisfactory, yet the Theory behind every religion remains completely self-contradictory and nonsensical. Paradoxically, only psychological Theories of religion (rather than theological ones) can make any sense of the phenomena, but you cannot make religions out of these, or can you?

As far as we can tell from archaeology, the Practise of Magic has continued since the dawn of human sentience, yet it remains a Practise in search of a Theory.

Underlying the Practise lies the reality that intent and imagination can make things happen. Exactly how this works has remained the subject of thousands of years of Theoretical debate.

The early Shamans modelled the effect as arising from the ‘spirits’ of animals and natural forces. Pagan magicians attributed the effect to the intercession of the gods and goddesses of their pantheons. Monotheist magicians attributed it to their god or to various of his angels, devils, and demons. Those three magical paradigms all also flirted with necromancy at times and invoked the supposed powers of the dead.

Materialist philosophies stimulated a new flowering of magical theory. Everything from magnetism to the supposed luminiferous ether supporting electromagnetic radiation became co-opted as a model or an analogy for the mechanism of magic. The discipline of parapsychology attempted to render magical effects objectifiable and repeatable but in doing so it removed most of the conditions under which they can manifest and it achieved little more than trivial probability distortions which tended to decline as the experimental setup itself drained motivation away. Magicians should remain thankful for the failure of parapsychology; they cannot convict us for it now.

Some magicians remain content with the ‘bare’ theory that intent and imagination can make things happen and do not overly concern themselves with the ‘how’. Others take a variety of views of entities and egregores and ‘spirits’ with some arguing for their separate independent existence and some arguing that purely mental constructs of such phenomena (tulpas) would have indistinguishable effects anyway.

‘Nobody understands quantum physics’ as Richard Feynman, one of our most noted quantum physicists, wryly observed. Nobody understands how magic works either, at present we just have formulae and recipes for making desired results more likely.

Quantum physics continues to offer the prospect of some sort of mechanism for the implementation of magical intent, perhaps they both work for similar reasons, perhaps not, but if they do, then the Theoretical elucidation of either may throw some light on the other and leads to improvements in the Practise of both.

Presently, a combination of the Psi-ontological realism of the PBR theorem with Cramer’s Transactional Interpretation of QM seems to offer some promise although it remains unclear how intention interfaces with this. 

Lockdown on a remote shore has involved some inconveniences but also some unexpected freedoms, like day long reading sessions and no showers for a month in order to conserve resources for cooking, (an old soldier once told me that you only ever need to wash armpits groin and feet, the rest takes care of itself - and so far so good).

With limited resources, culinary innovations can occur, I proudly present Tuna-Porridge, - breakfast of champions. Soak some oats for a few minutes in a small amount of water, add a tin of drained tuna flakes, season with chili sauce and whatever savoury herbs and spices you have. Heat with continuous stirring till it goes into a thick paste. Awesomely nutritious and filling and it tastes delicious. It would also make a great pie, pasty or flan filling.

The lack of a fully equipped shed at first seemed a concern, but beachcombing combined a little improvisation led to these: -

The Ankh topped Pyramid of Shub-Niggurath, plus a tetrahedron which doubles as a simplified Pentachoron.

The Elder Goddess Shub-Niggurath represents the Cosmic Biota. The Egyptian Ankh symbolises Life. The entire edifice signifies ‘The Intent of Life’, (A spell for hope in these dark times as Death stalks the land).

The Ankh-like iron bolt came from an ancient wooden shipwreck and needed a lot of tar removing from it. The pumice like stone may consist of volcanic pumice or lightweight composite building material wreckage that got washed in by the tide, grinding it away against a flat rock gave the pyramids their facets.

April Fool’s Day.

We have made fools of ourselves by expecting globalisation, urbanisation, population and economic growth, mass travel, and questionable techniques of intensive agriculture and the handling of domesticated and wild animals to have no severe epidemiological consequences.

How much of this behaviour will we resume after this virus crisis ends? Most of it probably, more fool us.

However, some may take the opportunity of enforced confined leisure to rethink just what and who in this life really matters to them. Will some become content to work less and to waste less?

It does seem that the severity of the symptoms of this virus can depend on the size of the infecting dose. If so, then social distancing makes more sense than ever, and we must doubly applaud the heroism of frontline medical and essential service personnel.

I have not wasted my time in lockdown, so now to celebrate this day, Hypersphere Cosmology (5), a self-consistent version at last? Please falsify it if you can, I welcome feedback and argument.

https://www.specularium.org/hypersphere-cosmology

This will surely make a great fool of someone, either me or the majority of the world’s cosmologists.

Keep conjuring for sunshine, in the literal, the metaphorical, and the metaphysical sense.

Replacing the Big Bang Theory.

The Big Bang Theory has dominated the scientific cosmology of humanity for the last half century, it has become the official scientific creation myth.

The so called Standard Model, or LCDM (Lambda-Cold Dark Matter) has the observable universe erupting from an infinitesimally small point of almost infinite density and temperature and then expanding to what we can currently observe over a 13.8 billion year period, driven by a mysterious inflation field and then by a mysterious dark energy (Lambda), and modified by a mysterious form of dark matter (CDM).

Most lay people seem to accept this with a vague sense of wonder and a shrug, well it sounds crazy, but the scientists assure us of its truth, in fact, they often become irritatingly insistent and almost religious about it.

Philosophically the theory sounds very unattractive and nihilistic for it implies that the universe began with a cataclysm and will end eventually in another or merely fade away to a diffuse entropic mist.

Several Philosophers have commented that the cosmologists who built this theory have taken such gross liberties with the scientific method that it does not constitute a proper scientific theory at all now. They have let unconfirmed hypotheses run away with themselves and forced the observational data to fit them, despite that this has led to a ridiculous proliferation of unconfirmed sub-hypotheses which merely render the whole edifice less falsifiable, not more accurate.

The LCDM-Big Bang theory has entered a crisis phase, it becomes increasingly difficult to fit the observational data into the model without first distorting it through a prism of assumptions which then become part of the theory. The theory has become path-dependent, having taken a wrong turning a long while ago when cosmological redshift became interpreted as recession velocity in a metric expansion of spacetime.

It seems analogous to what would happen if a complex quantitative theory of chemistry had developed on the old basis of earth, air, fire, water, and phlogiston, yes you probably could erect a theory based on this rather than on atoms and elements, but it would become ever more complicated and grotesque and full of sub hypotheses about the phlogisticated forms of fiery-air that have negative-earth. A similar thing happened in solar system astronomy centuries ago, in an attempt to preserve the earth-centric Ptolemaic system in the face of new observations, astronomers ended up creating a baroque system of Epicycles containing ever more circles within circles until the heliocentric model replaced the whole edifice at a stroke.

A seminal breakthrough has recently occurred in Hypersphere Cosmology. The apparently excessively fast rotation of galaxies turns out not to arise from the presence of a mysterious and otherwise undetectable substance dubbed ‘dark matter’ which has by now become woven into the fabric of the fraying tapestry of the LCDM model. Rather, this excess rotation arises from the same mechanism which prevents the collapse of the hypersphere of the universe.

v(r) = v_i(r) + wr

Where v(r) means the rotation velocity of a galaxy at radius r.

And v_i means the rotation velocity of a galaxy at radius r expected from the observed distribution of the ordinary matter within it.

And w means an angular velocity peculiar to each galaxy, which when multiplied by the radius r and added to v_i gives the observed rotation.

This comes from the work of Roy Gomel and Tomer Zimmerman 2019

https://www.galaxyrotationcurves.com/

https://www.preprints.org/manuscript/201908.0046/v1

It struck me that the w factor equals an angular velocity component posited for any dust like cloud of gravitationally bound matter in the work of Kurt Gödel 1949.

https://journals.aps.org/rmp/pdf/10.1103/RevModPhys.21.447

w = 2 sqrt (pi G d)

Where for a galaxy, the density d needs to include the entire ordinary mass of the galaxy and the entire volume of the spherical gas halo around it.

Thus, finally;

The Galactic Rotation Equation: -

v(r) = v_i(r) + 2 sqrt (pi G d) r

This equation works well for the closer galaxies where we can actually observe their gas halos.

Example calculation here: - https://www.specularium.org/component/k2/item/290-rotation-of-the-triangulum-m33-galaxy

Gödel acquired immortal fame for his Incompleteness Theorem (and his profound eccentricity). Now perhaps his largely ignored 1949 paper which derives angular velocities from Einstein’s Field Equations of Relativity will also find its place in history.

This elegant solution solves the problem of galactic rotation curves without invoking a mysterious ‘dark matter’ or by modifying Newtonian or Relativistic dynamics.

With all the main principles and equations in place and in alignment with observational data now, (The Hypersphere Equation, The Hypersphere Vorticitation Equation, The Redshift-Distance Equation, The Hyperspherical Lensing Equation, and the Galactic Rotation Equation, and so on), the LCDM-Big Bang Theory now looks finished and due for replacement by a Hypersphere Cosmology. This looks simpler and more philosophically satisfying and it has greater predictive power. Academically respectable looking papers will have to get past the peer reviewers and censors who guard the gates of prestigious journals. This may take a while.

Cosmologists can then spend the following decades exploring the consequences of the new paradigm. As it contains an element of Gödel that may include some form of time travel or retro-causation.

My thanks to those who have followed these threads over the years, indulged the many speculations and mistakes, and got in touch with encouragement, mathematics, and corrections. The wastepaper basket remains the theorists most powerful tool as Einstein observed.

Einstein appeared to have lost the argument with Lemaitre and retracted his Cosmological Constant, describing it as his greatest blunder, and he accepted the expansion hypothesis instead.

Nearly a century of increasing baroque cosmological nonsense resulted from this as theorists attempted to force an interpretation of every new item of observational data into the expansion paradigm.

If Einstein had looked more closely at Gödel’s metric, he might have realised that between them they had got the basics right - the first time.

Incidentally, the cracks in the LCDM-BB model just became fatal wounds: -

https://www.nature.com/articles/s41550-019-0906-9

(The data from the Planck satellite now strongly indicates a closed spherical universe.)

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.081803

(Insufficient matter-antimatter asymmetry exists for the universe to have arisen from a Big Bang.)

A considerable number of mopping up operations remain until LCDM-Big Bang theory unconditionally surrenders to a Hypersphere Cosmology. Yet we have arrived at the beginning of the end and can start reinterpreting all the awkward interpretations of observational data that disfigure the LCDM-BB model and build a better one.

I hope to participate in that process but also to devote time to making better sense of the current mess of interpretations of Quantum Theory. Hypersphere mechanics and three-dimensional time may have a part to play here. May Azathoth grant me the time and the inspiration.

Few things seem to bring more relaxation, refreshment and relief from the rigours of the library, the conjuratorium, the laboratory, and the scriptorium than some hours spent in the shed of Chateaux Chaos.

This emerges in celebration of the completion of the project: -

It has the look and feel of calcedony yet it consists of [NH-(CH₂)₅-CO]_n just four elements, mainly gases, polymerised to make what we commonly call Nylon. As a sculptural material it has interesting properties, translucent and rather like a heavy hardwood but without the grain, it absorbs surface dyes quite readily. Apparently, you can also melt and cast it at some risk, I may give that a go.

This wand bears the sigils and notae of The Hypersphere, Apophenia, and Yog-Sothoth on its facing facets. (Consult the EPOCH for details). 

Religion usually proves useless in the face of plague, however I did notice that an enterprisig church had placed in the entrance to its graveyard, an honesty box, a pile of shovels, and a big notice saying 'Dig Your Own - £50' 

Conjure for clear skies, sunshine, and hot weather. It may help with the situation. With the aircraft contrails mostly gone now it should become easier.

Galactic Rotation Curves.

A large discrepancy exists between the rotation curves for disc galaxies expected from a classical or relativistic consideration of their baryonic mass distributions, and the rotation curves observed. This discrepancy has led to the hypothesis that a mysterious ‘Dark Matter’ must make up the difference.

Gomel and Zimmerman show that an apparently ‘Non -Inertial System Component’ in the form of an angular velocity ‘w’, can account for this discrepancy.

v(r) = v_i(r) + w(r)  

https://www.preprints.org/manuscript/201908.0046/v1

This paper asserts that the angular velocity w arises from a Gödelian rotation component of the galaxies where w = 2sqrt (pi G p)

https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.21.447

 ‘Matter everywhere rotates with an angular velocity of twice the square root of pi times the gravitational constant times the density.’

Thus, v(r) = v_i(r) = 2sqrt(pi G p)  r

Now because the wr component of galactic rotation dominates at the extremities of galactic discs, thus creating ‘flat’ rotation curves, and because the outer edges of all disc galaxies rotate with the same time period of almost exactly one billion years, irrespective of their varied sizes.

https://astronomy.com/news/2018/03/all-galaxies-rotate-once-every-billion-years

It follows that we can calculate w with high accuracy to w = 2 e-16 radians/second.

Calculation:

distance/velocity = time

2 pi r / wr = t

2 pi / 2 e-16 = t

pi e16 = t = 3.142 e16 seconds.

(A billion years equals 3.155 e16 seconds)

Thus, it seems far more likely that all disc galaxies have a Gödelian rotational component of precisely 2 e-16 radians/second rather than dark matter halos with sizes and masses precisely and mysteriously tailored for each galaxy’s distribution of ordinary baryonic matter to create the observed rotation curves.

Peter J Carroll 13/02/2021

Februlog.

Esoteric Horticulture.

Finally, eight years after the planting of her seed, Circe, the largest of the three Mandrakes at Chateaux Chaos, has given birth. See the fruit of her labour below.

These somewhat antinomian plants (Mandragora Autumnalis), prefer to flower in autumn and to produce fruit in spring. During summer they shrivel back to their huge humanoid bifurcated taproots. Perhaps they do this to avoid insect pests or desiccation during the hotter months in their native Mediterranean lands.

I don’t think they like it here on this chilly island, but I’ll distribute the seeds amongst some Druids with instructions for their nurture.

Alternative Physics.

Below see a couple of graphs based on the observational data of a substantial number of Type 1A supernovae at various Redshifts. We can measure Redshifts with great precision but Apparent Magnitudes, particularly of transient events, much less precisely.

The blue line shows Apparent Distance at various Redshifts. Here I derive Apparent Distances from observed Apparent Magnitudes by converting Apparent Magnitudes to Fluxes and then applying the inverse square principle (taking the Magnitude of a Type IA supernova at 10 parsecs with negligible redshift as a baseline).

Clearly, any luminous object with a high Redshift will have a ridiculously vast Apparent Distance as the graph curves upwards. Herein lies the basic peculiarity that led to the hypothesis of ‘Dark Energy’ powering an apparent acceleration of the expansion of the universe.

The orange line shows Actual Distances against Redshifts. Here I derive Actual Distances from Apparent Distance by applying a Hyperspherical Lensing Formula based on the principle that we observe the Hyperspherical Universe in Stereographic Projection because of it positive spacetime curvature.

The derivation of this Hyperspherical Lensing Equation appears in section 7 here: -

https://www.specularium.org/hypersphere-cosmology

In this graph redshift 1 corresponds to half antipode distance and the distances to far supernovae become much more reasonable. The graph shows that the universe will have an antipode distance very close to 13 BLY.

The Universe does not expand, let alone does it have an accelerating expansion, so called ‘dark energy’ does not exist.

Great! The universe remains eternal, we can abandon the philosophical burdens of an apocalyptic beginning or ending to it.

Also see this https://www.specularium.org/component/k2/item/290-rotation-of-the-triangulum-m33-galaxy

Perhaps the final end of so called Dark Matter.

Magic/Culture/Politics

Identity and Individualism in the Pandaemonaeon.

A wandering Scholar dropped in for an evening last week. Forced to compete in an oversubscribed tournament profession with zero security of contract he seemed underpaid and underemployed. A Professor did recently mournfully describe to me how a vast new exploited Academic Proletariat had arisen.

I suppose this class of Scholars must account for the tsunami of usually rather inconsequential esoteric papers which now appear daily on Google’s Academia.com. It boasts 114,376,069 Scholars and counting.

We had a lively discussion till late about many matters Magical, Cultural and Political, touching on everything from the weird phenomenon of Professor Patricia MacCormac https://en.wikipedia.org/wiki/Patricia_MacCormack to Populism, a world going apparently mad, and my part in this.

All this behoved me to check my predictions for this era.

The Psychohistoric Mechanism of the Aeons, discovered in 1988 and published soon after in my Liber Kaos, predicted the Pandaemonaeon - an era characterised by the ascendancy of Scientific and Magical Thinking and the nadir of Art and Religion. It seems to have come upon us rather quickly, assisted by globalisation and the internet.

Mind you, I didn’t say that everyone would necessarily like the Pandaemonaeon. On a broad raft of criteria some sociologists conclude that quality of life peaked in the technically developed world somewhere around the 1970’s and that dissatisfaction has risen since. Most people have more stuff, but they don’t seem to get any more satisfaction from it and their lives have become ever more frantic, complicated, and insecure.

Religion has largely ceased to engage with transcendental concepts. Theology (which always meant politics in the broadest sense) has now become overtly political, and religion now acts as little more than a social group identity badge. Religion no longer tells us a story about our inner self(s), it merely tells us which groups we belong to or despise.

Since humanity achieved the wealth and the technical ability to produce Art to any required degree of beauty and brilliance, Modern Art has abandoned any quest for meaning or spiritual uplift and now celebrates the empty rubbish of those whose talents remain limited to self-promotion, on the contra-intuitive principle that it must contain something worthwhile because of the price tag, even if we lack the wit to see it. Modern Art no longer tells us a story about human aspiration, at its best it merely illustrates human folly as artists become the keepers of useful sarcasms, along with our philosophers. Only the amateur and commercial art which does not attempt to mimic modern art seems to have anything interesting to say.

Science now tells us the dominant story about ourselves. We exist as randomly evolved mortal animals with unusually large brains, on an unremarkable planet in a stupendously vast universe. Deal with it.

Whilst I question the current official scientific creation myth (the Big Bang hypothesis), I do accept the above and I find the scientific story both liberating and exhilarating. I consist of the totality of what I do. I have no mysterious ‘real self’ or inner ‘being’ to worry about, but a lot of people seem to think they must have such a thing and today imagine that they express it through Identity and Individualism.

Yet the demands of individualism begin to outstrip supply in a demand-based consumer economy, and it becomes increasingly difficult to become a genuine eccentric as all eccentricities become Identity brands in a hyperconnected society.

The State has taken over so many of the legal and financial functions of the Family that few people now identify strongly with their Familial or Tribal status beyond what remains of it in the nuclear family.

Regional identities now seem quaint and faintly ridiculous in an era of mass travel and mass communication. Sports teams supposedly representing ‘our’ cities now draw most of their managers and players from distant cities and continents.

In an era in which we think we know so much, Nationalism and Patriotism have become unfashionable because few people particularly like their own governments or the way they run the country, they just despise other countries more, so they do not usually wish to define their Identity by it.

(The European Union has failed to raise any vision of a European Identity beyond that of an unloved common bureaucracy.)

Nobody really believes in anything about themselves. We have become Lost in the Cosmos, with no metaphors for self, we just have choices of individualism and identity, and mass exposure to everyone else’s assigned or chosen identity.

Individualism in the age of Identity centres on trying to control how others regard you, not on how you regard yourself(s).

We must suspect those who preach their Identity loudest harbour the most doubts.

In this Pandaemonaeon, Identity/Individualism has become the Religion of the age because it has become fragile and mutable.

We now find ourselves passing laws to prevent anyone criticising anyone else’s Identity.

Such laws represent the official theology of the religion of Identity.

The UK police now seemingly devote more resources to investigating everything on the spectrum from ‘hate crime’ to ‘mild disdain crime’ whilst theft, fraud, and violence frequently seem to go un-investigated.

In the new religion of identity, the cult of celebrity provides a rolling pantheon of minor deities that we adulate for a time and then discard or crucify with guilty pleasure.

The culture wars that rage within our societies, the polarisation of opinions, the rise of currently fashionable forms of victimhood and mental illness, the usually secret and officially sinful pleasures of despising other people’s identities may all find their roots in the paradoxical relationship of Identity to Individualism and the increasing fragility of both.

Today we expect all of an individual’s opinions to conform to a recognisable identity.

Extreme left, hard left, centre left, centre right. hard right, extreme right. Social liberal, social conservative. Economic liberal, economic conservative. Racist, culturalist, cultural-relativist, multiculturalist, anti-racist. Rights-based moralist, responsibility-based moralist. Social Darwinist, socialist. Theocrat, militant atheist. World destroying kapitalist, extinction rebellionist. Carnivore, vegan.

Express an opinion that someone considers to fall within any of these categories and they expect you to hold all the opinions that they think necessarily go with it. Of course, none but extremely right-on woke-ists or those right-off the other end of the scale hold opinions of such imagined coherence. Hitler practised vegetarianism for example.

The ascendancy of Magic in the Pandaemonaeon often passes completely unacknowledged unless you realise that the bottom line of magical thinking comes down to: -

                                                    ‘Thinking Makes It So’.

This may seem a completely deluded idea, but if handled skilfully it has enormous power.

Positive thinking can lead to extraordinary achievement, if you believe you can do something you increase your chances of accomplishing it. Negative thinking has similarly powerful effects, you can sabotage any venture with it. Placebos which we expect to work often have effects as great as treatments based on rational theories, and so do Nocebos. Curses and supposed pollutants which rationally should not have effects, can have quite damaging ones.

Thinking that you have helpful spirits on your side often gives you an edge over those who don’t, particularly for those who made such spirits deliberately and magically.

Labelling phenomena by their supposed ‘essences’ makes it easier to agree or disagree with others or to persuade others about them.

The bullshit believed about any product tends to make it sell better than its objective properties. This applies to all commodities, - religions, scientific hypotheses, political parties, celebrities, and individuals.

We live in an era where commercial, political, and personal ‘fake news’ and propaganda dominate communication. We generally prefer this now because in conditions of massive information overload, most simplifications become welcome in themselves or afford us the pleasure of contradicting them.

The magical ‘Thinking Which Makes It So’ requires considerable skill and experience. Not everyone can write persuasive propaganda or advertising copy or even convince themselves of something without practise and help.

The pandaemonaeonic magician can hold mutually contradictory opinions and beliefs on a situational basis for pleasure and profit. Free from the illusion of unitary Identity and the struggle to maintain and defend one, the magician remains inwardly aloof in a fortress of supreme arrogance built upon the meta-belief that beliefs and actions shape reality.

The effects can seem parapsychological.