Abstract.

This paper presents a quantitative equation for Mach’s Principle that appears to satisfy the requirements of most of the qualitative expressions of Mach’s Principle, and it suggests that the universe has spatial closure and a Transactional gravitational exchange mechanism.

Mach’s Principle.

We recognise mass as having two familiar components, firstly inertial mass – a resistance to acceleration as quantified by Newton’s second law that force equals mass times acceleration, shown here by denoting the mass involved as the inertial mass.

Secondly mass also exhibits a gravitational effect, any two masses appear to attract each other with a force described by Newton’s equation of gravity. In this, the force between a mass m (usually a large mass like a planet or a star) and the mass of interest depends on both masses, the gravitational constant G, and the square of the distance between them. He we denote the mass of interest (which usually means the smaller one that falls or moves most) by its gravitational mass

Now in Newton’s theory, inertial mass  miraculously seems to exactly equal gravitational mass  and this equivalence explains Galileo’s observation that all masses fall at the same rate.  Thus although a heavier mass has more inertia and needs more force to move it, its greater mass gives gravity an exactly proportional extra amount of gravitational mass to work on, so to speak, so all masses fall at the same speed.

On the human scale, inertial mass often seems intuitively ‘stronger’ than gravitational mass, we can feel the resistance a cannon ball offers to our pushing it around, but we cannot feel the gravitational attraction between it and ourselves. This arises because the ‘ratio’ between gravitational mass and inertial mass has a very small value represented by G, the gravitational constant. Nevertheless, the ratio remains constant and an amount of material that has a certain amount of inertia will always have a certain corresponding amount of gravity.

Now Einstein saw something deeper and beyond mere convenient coincidence in the equivalence of inertial and gravitational mass (or more precisely in the equivalence of acceleration and gravity), and he reformulated our ideas about gravity.

He described gravity not as some sort of force at a distance but as an effect arising from the curvature of spacetime by mass. Thus, a massive object like a planet curves spacetime about itself and freely moving objects all follow this curvature by falling towards it at the same rate, and they do not actually feel any forces at all whilst in free fall.

‘Spacetime tells matter how to move; matter tells spacetime how to curve.’ As John Archibald Wheeler so elegantly summarised the idea of General Relativity.

The description of gravity as spacetime curvature gives far more accurate predictions than the basic Newtonian model but it does not say much about the inertial component of mass. In the Newtonian model, inertial mass just appears as somehow intrinsic to an object and gravity appears as a mysterious ‘force at a distance’. Neither of these ideas sits comfortably with the relativistic perspective in which properties arise on a relational basis.

Mach's Principle has hung around on the fringes of cosmology and relativity for 100 years, it has influenced a number of theorists but nobody seems to have managed to formulate it concisely or to develop some maths for it. Roughly speaking it suggests that the inertial mass of any object arises because of the effect of all the stuff in the entire universe, so as Mach put it, if the subway jerks, the far stars and galaxies throw you to the ground

This idea has lurked within physics since Einstein named it after some remarks by Mach (who devised the Mach numbers for multiples of the speed of sound). Nobody appears to have found a way to quantify it and various qualitative versions of it exist. It broadly states that some relationship should exist between the inertia of any body and ALL of the rest of the material in the entire universe. This would seem to imply a spatially closed universe, otherwise inertial mass, and many of the laws of physics, would vary with time.

Debate rages about whether General Relativity really incorporates Mach’s Principle or not. The currently most popular interpretation of cosmological observations asserts that the universe expands from some sort of a big bang, in which case Mach’s Principle seems invalid unless inertial masses either vary with time or remain invariant to the distribution of matter within the universe. As it appears that the distribution of matter in the universe always remains homogenous on a large scale, this distribution invariance comes down to an invariance to the size of the universe which seems highly unlikely as  the spacetime curvature we recognise as gravity remains very much distance dependent.

Now if the inertia of any object depends on the entire rest of the universe then it must depend on the gravitational mass of the body in question, the gravitational mass of the entire universe, the Gravitational constant that relates them, and the size of the universe, and the speed of light. Moreover, the ratio of inertial to gravitational mass must remain constant as we have every indication from astronomy that it has not varied over the observable history of the universe.

Now in Hypersphere Cosmology¹ , which posits a non-expanding universe: -

Where G = The Gravitational constant

               M = The Mass of the universe

               L = The antipode distance in a hyperspherical universe

               c = The speed of light.

This strongly suggests that the following equation quantitatively fulfils the major qualitative requirements of most expressions of Mach’s Principle.

If the gravitational constant of the universe or the mass of the universe were to increase so would all inertial masses, conversely any increment in the size of the universe or lightspeed would decrease all inertial masses.

GM/Lc^2 thus appears as a sort of scalar field, omnipresent and apparently non-local* in the hypersphere of the universe, and giving rise to an acceleration A = GM/L^2 which has detectable effects such as the Pioneer anomaly and the anomalous galactic rotation curves.

(See Hypersphere Cosmology¹ )

At present the equation has no practical use except to complete hypersphere cosmology because there seems no way we could currently manipulate the effects of G,M,L, or c, in the vicinity of a spacecraft, but if we could reduce inertial mass somehow then we could easily move matter around the universe.

*The apparently instantaneous effects of both inertia and ‘static’ gravitational spacetime curvatures raises interesting questions. Gravitational waves undoubtedly propagate at light-speed from accelerated masses as Einstein predicted and as recent experiment has confirmed.

If we accept that nothing can travel faster than light then the apparently instantaneous effects of inertia and static spacetime curvatures, (gravity ‘fields’) may arise from a Transactional Exchange between curvatures. The laws of gravity seem completely time symmetric and capable of supporting advanced negative curvatures propagating down retarded positive curvature paths back into the past to create apparently instantaneous effects.

The time-symmetric nature of all physical laws except the Second Law of Thermodynamics (which states that in an isolated system Entropy will increase only) at first appears very mysterious and physicists usually quietly ignore the time reversed solutions to their equations and calculations.

Hawkin remarked that ‘Entropy increases with Time because we measure Time in the direction in which Entropy increases’. We have no way of telling in which ‘direction’ ‘time goes’ or even if it actually ‘goes’ anywhere.

If however, we adopt the Transactional Interpretation and extend it beyond quantum physics to gravitation and to model gravitational effects as arising from positive spacetime curvatures propagating forward in time and negative spatial curvatures propagating backwards from the future to create effects in the present then we can explain the apparently instantaneous effects of inertia and static gravitational ‘fields’.

Of course, the same argument applies to electrostatic fields that would then correspond to a special class of spacetime curvatures.

Accelerations of masses and electrostatic charges will of course create disturbances in spacetime curvatures that propagate at light speed as bosons with the wave –particle duality characteristic of quanta. However, the concept of virtual bosons mediating static gravitational and electrostatic interactions becomes redundant.

Reference¹.

Hypersphere Cosmology 2. Author: Peter J Carroll. http://vixra.org/abs/1601.0026

After the discovery of the cosmological redshift, Einstein retracted the cosmological constant that he had devised to stabilise his static hypersphere model of the universe, describing it as his greatest blunder. It does indeed look like a bit of an ad-hoc fudge factor in the form in which he inserted it into his equations. He considered it effectively as a source of anti-gravity of unknown origin that prevented the hypersphere collapsing in on itself. Einstein went over to the expanding universe model, but the recent discovery of a mismatch between supernovae redshifts and apparent magnitudes has led to the idea of dark energy driving an accelerating expansion of the universe which implies a resuscitation of the idea of a cosmological constant, some have opined that his ‘greatest blunder’ lay in abandoning his original idea.

Gödel attempted to stabilise the Einsteinian hypersphere by having it rotate. His cosmological constant appears as an angular velocity. However, as no axis of rotation seemed observable this solution also fell into disuse and obscurity.

The Hypersphere Cosmology model also arises from the original Einsteinian and Gödelian models but it looks further into the geometric properties of hyperspheres which have an intrinsic form of rotation (vorticitation) with no observable axes and which give rise to a type of cosmological constant expressed as a negative acceleration A, that stabilises the hypersphere at constant size, redshifts light on cosmological scales, increases the orbital velocity of rotating galaxies, and lenses the light from distant supernovae distorting their apparent magnitudes.

Intriguingly, all three cosmological constants exhibit a stunning equivalence as the final equation in the above shows.

Most alternative cosmologies tend to pose the question ‘What if Einstein got it wrong?’, Hypersphere Cosmology poses the question ‘What if Einstein and Gödel actually got it pretty well right the first time?’

Esoteric Horticulture

I have finally abandoned all doubt about the reality of Global Warming. After our bizarre spring and summer my three Autumnal Mandrakes woke up and sprouted at the autumn equinox rather than wait for Samhain as customary. So many other plants have seeded prematurely that the squirrels and birds have hardly bothered with the bird feeders.

Soon an eight-foot votive pillar to Cuda the Celtic Goddess of the Cotswolds (Cudaswolds?) will appear in the gardens. Her popularity amongst neo-pagans has shot up in this part of the world since the discovery of a Romano British plaque, apparently to Her, near the local Celtic capital of Cirencester. However, the Prof informs me that the whole modern myth derives from the recent very imaginative and questionable work of the amateur archaeologist Stephen Yeates and that it all looks like a splendid example of Chaos Magic. Deities ‘R Us!

Politics

The shitstorm of conflicting opinions, passions, and predictions about Brexit continues and the questions about the competence and integrity of all our politicians mount.

Nevertheless, let us never forget that the British voted in favour of deciding on their own response to globalisation and immigration rather than accepting the diktats of others that they did not elect on these matters – whatever the economic costs or benefits.

The EU surreptitiously mutated from an economic into a political project. Any new vote to remain would effectively mean a vote to deprive ourselves of the right to ever vote again on anything important. The British Parliament would become as much of a sham as the European ‘Parliament’.

Square Rigger Chess models the manoeuvre and combat of square rigged naval ships of the Napoleonic period. No element of chance enters into this system, the results depend entirely on player skill and the chosen starting conditions, to this extent it functions as a chess-like game. This modelling system depends on several simplifications for game play: -

The division of sea areas into squares. The orientation of all ships and firepower and wind direction, in just 8 possible directions. The characterisation of ships by just 3 factors, Firepower, Speed, and Turning ability. F, S, and T.

Firepower. – (the combined effects of cannon + carronades + mortars + musketry), ships begin with a firepower factor of 2, 3, 4, or 5. In attack a ship may allocate its firepower factor in any directions preferred up to the maximum of its firepower as shown in the Fire chart following: For example, a 2^Nd Rater with a firepower of 4 could direct all its firepower of 4 in a starboard (right) or port (left) broadside, but not both. It can only use a maximum of 2 units of its firepower (4 – 2 = 2) fore or aft and only a maximum of 3 units (4 – 1 = 3) off the port or starboard bows or off the port or starboard stern, thus it could for example simultaneously fire 2 units of its firepower fore and the other two off the starboard bow, (or any other direction chosen). In combat the attacker assigns firepower factors to chosen directions first.

The effect of attacking firepower falls off with distance, by 1 per every square after the immediately adjacent square effect shown below. (See the Distance Fire Chart later.)

Ships defending against Fire use their Firepower factor in the same way, assigning part or all of it to various directions to try to cancel the effects of incoming fire, however it does not decrease with distance. This curious seeming rule reflects the fact that the vulnerability of ships rose in precisely those directions where they could use the least of their firepower.

Any ship which receives from any direction more firepower than it assigns to that direction takes one ‘Hit’ for every unit of firepower that it loses by. Merchant ships have defensive ‘firepower’ only.

Speed and Turn. In a player turn ships may move one square forward for every Speed factor they have and may turn 45 degrees (one eighth of a full circle) for every Turn factor they have.

The chart below shows what manoeuvres a 3^rd Rater with a Speed of 2 and a Turn of 2 can do in a move with mainly starboard turns.

The nimble 3^rd Rater starts on square 1, its initial position shown in black. It can end its move in any of the positions shown by red ships by using some or all of its 2 Speed and 2 Turn capabilities. Note that it could also use turns to port instead of starboard to end up in the positions and orientations shown by the white ships and that it could also make other orientations on squares 4 or 7 using turns to port. (Not shown).

The heavier ships have less manoeuvrability than a 3^rd Rater, and manoeuvrability declines as ships take Hits (see damage chart).

Wind direction and intensity also affect manoeuvrability (see wind rules and chart).                                                                                   

Ship Classes.

First Raters. F5, S1, T1. These rare lumbering behemoths with 100+ guns have huge firepower but poor speed and manoeuvrability.

Second Raters. F4, S1, T2. As above but these monsters with 84 guns do manoeuvre slightly better.

Third Raters. F3, S2, T2. These faster and more manoeuvrable 64-gun warships serve as the main workhorses of the line of battle.

Frigates. F2, S2, T3. These fast and highly manoeuvrable 44-gun warships can bring vital extra fire support when heavier ships engage.

Distance Fire Chart.

Firepower has its greatest effect into adjacent squares, but ships may also use their firepower at greater distances. Basically, subtract one from the effect of assigned firepower for each additional square. Thus, if the vessel below has a firepower of 4 and assigns it all to a starboard broadside that broadside can only have an effect of 3 on any one square marked X, or 2 on any one square marked Y.

The Non-Adjacency Rule. Ships on the same side must leave at least one empty square (orthogonally or diagonally) between themselves when ending their player moves.

This rule may seem slightly unrealistic, although friendly ships did try to keep at least a ships length between themselves.

This rule allows for the use of the classic manoeuvre of ‘cutting the line’ without the complications of modelling collisions. Ships on opposite sides can occupy adjacent squares, and they will often do so to disrupt enemy formations and to direct the fire of several ships to a single target.

The above chart shows a flotilla of red ships engaging a flotilla of blue ships. Note that whilst several ships from either side have moved to squares adjacent to enemy ships, no two ships on the same side lie orthogonally or diagonally adjacent to each other.

The non-adjacency rule does not apply inside of harbours, friendly ships may moor and manoeuvre alongside each othear, ships may also lay adjacent to friendly ships that have struck their colours.

Damage Chart. As ships take Hits, their Firepower, Speed, and Turning abilities decline as shown on the following chart. Players should place damage markers on their ship markers as appropriate to show their status.

Any ship reduced to 0 0 0 ‘Strikes its Colours’ and remains immobile and inactive for the rest of the battle and subject to towing away for repairs or as a prize afterwards, if the victor has a mobile ship spare to do this, otherwise the victor may elect to scuttle it.

Wind Chart. Players set the wind direction and intensity before play, the wind can come from any one of 8 directions. Players may also make some provision for a change of wind during the game if desired.

Moderate Wind simply prevents movement directly into the wind (square riggers could not do this), however they can turn into the wind and then turn to 45 degrees to the wind and effectively tack in a zig zag in a generally windward direction.

Stronger winds also deny movement directly into the wind and additionally allow for greater movement with the wind as shown in the chart below. The numbers on the squares represent the number of squares a ship can move in that direction for the expenditure of a single speed point. Ships can move twice as far with a following stronger wind.

General notes on scenarios and tactics. Players should practice with small numbers of ships at first. Larger flotillas and fleets may require the command of several Commodores or Admirals each in charge of a squadron, as coordinating the movement and fire of many ships becomes a challenging task.

Scenarios can include convoy interception (see note on transports and merchant ships), chasing down and capture of slow enemy heavy ships by more numerous lighter ships, harbour blockades and attempted breakouts, and fleet battles for naval supremacy.

Transports and Merchant Ships usually effectively consist of unarmed versions of naval ships, with the heavier ones having less speed and manoeuvrability. They take damage and strike colours in the same fashion.

Play takes place by alternate moves. In each player move players may move all their ships in any order so long as the final positions of their ships does not break the non-adjacency rule. Attacker and defender then both assign firepower in exchanges of fire, calculate Hits and place damage markers.

The following 2 charts show for extra clarity, firstly the effects of fire from diagonally orientated ships, and secondly the effects of stronger wind from diagonal directions.

Shore Batteries. These defend harbours and effectively act like static ships with high firepower. They should have precisely designated fields of fire. They take firepower damage in the same way as ships.

Commanders should learn to recognise the lines of squares which stretch out from the port and starboard bows and the port and starboard sterns of any ship, for these represent the ‘true diagonals’ of the ship itself, (whether the ship lies orthogonally or diagonally on a square), for these define its fields of fire and defence.

Note that Frigates begin with no ability to fire directly forward from their bows, or directly backwards from their sterns, and no defence against fire from these directions either. Theoretically negative values for defensive firepower do not invite extra damage hits, negative values simply count as zero. 

Politics

Globalisation and Immigration continue to fracture the landscape of British politics, and much of that in continental Europe as well.

Britain successfully integrated many waves of immigrants in the past because of the strength of its institutions and culture and because no immigrant group ever represented more than one or two percent of the entire population. Few people now even notice the 25,000 Axis POWs who chose to remain in the UK after WW2. However, as the proportions have increased, particularly of groups with cultures very different to the British model, the resistance to integration has risen exponentially on both sides. Thus, we come to the Unmentionable Elephant in the Room of which few dare to speak: -

Half the British voted for Brexit partly because of the issue of Non-EU Immigration. They didn’t want any more immigrants with conflicting cultures from Africa or Asia much more than they wanted to reduce the flow of eastern Europeans from the EU which merely depresses wages a little.

So now we have a weirdly distorted political landscape in which the centre has faded from view and opinions have polarised along strange axes.

The hard left continues its takeover of the Labour Party, having somehow sidestepped the antipathy to authoritarian and misogynistic Islamic culture that you might expect of the left, it has adopted an anti-Israel and anti-Semitic stance to attract the 6.3% Islamic share of the UK electorate. Plus of course the loony lefties also despise the Jews for their generally high levels of material success and intelligence.

The hard right meanwhile continues its takeover of the Conservative Party largely because of the unmentionable Elephant in the Room and the disastrous failure of multiculturalism.

So, politics as usual, with all sides obfuscating their real motives and wilfully confusing culturalism with racism.

Globalisation will inevitably encourage further huge waves of Africans and Asians seeking to emigrate to Europe. Brexit will only stop those using continental Europe as a stepping stone to get to Britain.

Only by withdrawing from the UN Convention of Human Rights as well can Britain regain control of its borders.

Alternatively, we could simply do what Australia and the Visegrád nations do, build good defences and let well briefed border guards sort the issue without resort to legal technicalities.

Magic

After a leisurely summer spent debating the finer points of magical philosophy and belief, a new practical course now begins on Arcanorium College: - One Wand, Three Enchantments.

Participants will attempt to create functioning versions of all four.

Physics

Gödel derived an exact solution to the field equations of general relativity for rotating matter: -

“Matter everywhere rotates relative to the compass of inertia with an angular velocity equal to twice the square root of pi times the gravitational constant times the density.”

My calculations show that an application of this formula to black holes or gravitationally closed hyperspheres of any size leads to velocities at the surfaces of these bodies which exceed lightspeed. This may not matter so much for hyperspheres with surface escape velocities theoretically in excess of lightspeed, but it may add an additional and much greater long-term instability to black holes than Hawking radiation. This matters very much to me as I don't want pesky black holes eventually gobbling up all the matter in a universe otherwise hyperspherically finite and unbounded in both space and time.

Book Review

Dark Star Rising – Magick and Power in the Age of Trump. Gary Lachman.

This book argues that Chaos Magic has made Donald Trump POTUS and that it also made Vladimir Putin Tsar of Russia with the Chaoist Alexander Dugin as his Rasputin. However, the author (an American) barely mentions the role of Chaos Magic in the accomplishment of Brexit. Nevertheless, the book does provide a comprehensive introduction to some of the principles and practices of Chaos magic.

Most if not all political initiatives grow out of shadowy or ‘occult’ beginnings in the realms of fringe religion, philosophy, and metaphysics.

Chaos Magic provides a philosophy and a technology for encouraging rather improbable and unlikely events to occur. Its technical theory predicted the advent of the Pandaemon-aeon well in advance of its current phenomenisation. However, Lachman only quotes Liber Null, so perhaps he didn’t notice the Aeonics material in Liber Kaos. For some source material on the origins of Chaoism he resorts to the second-rate scholarship of Dave Evans who, after failing to get an interview (nobody liked him) simply googled existing disinformation to bulk out his lame PhD thesis.

In this new Pandaemon-aeon, Nothing has Truth and Everything remains Possible. Intent and Imagination trump ‘facts’, expert opinion, and probability, and we make up ‘reality’ as we go along. 

Lachman explores at length the careers and occult antecedents of notable demagogues such as Hitler and Mussolini, yet these deplorables took their cues from the Nietzschean and Crowleyesque occult philosophy of the Triumph of the Will, rather than from the Chaoist Triumph of the Imagination.

Lachman also digresses at length upon various ‘spiritual gurus’ who have mastered the skill of exploiting some peoples need to have meaning and authority imposed. In this he perhaps doesn’t go far enough, as anyone spouting ‘spiritual wisdom’ spews only lies and bullshit.

Chaos Magic never became an exploitative religious or political cult itself despite a couple of (failed) minority attempts to develop such things within or alongside it, precisely because it gave away the secrets of how to do this to all commers, thus proofing them against it.

Lachman notes that the occult seems mainly associated with right wing political initiatives although he mentions the so far ineffectual Witches against Trump campaign. The liberal centre and left seem to have missed a trick here in recent decades by presenting their ideas in purely rationalistic terms lacking in imaginative glamour and charisma. By allowing vociferous minorities to write the book on politically correct thought-speech, the liberal centre and left have handed the radical right the opportunity to present themselves as heroic free-thinking rebels.

That mystically inspired conservative initiatives can, with the passage of time, mutate into an equally oppressive materialistic liberal absolutism may come as a surprise to many, so it seems refreshing that Lachman details the Synarchy or ‘Total Rule’ philosophy lurking within the European Union project.

Overall, Lachman has written a fascinating analysis of how esoteric and occult ideas have had political consequences, without descending too far into the murky pits of conspiracy theory.    

Addendum

Chaos Magic has enlarged humanity’s toolkit, what will we eventually do with it?

Destroy all monotheist religions and create more amusing personalised ones for ourselves?

Achieve Chaocracy – government by randomly selected committees of citizens?

Overcome the almost universal scientific belief in the expanding universe hypothesis?

Achieve the five zeros – zero population growth, zero CO2 and pollutant emissions, zero resource depletion, zero economic growth, zero loss of life satisfaction.

Imagine!

Recent research on Arcanorium College into Magical Thinking in general has thrown up some interesting insights into its contemporary use in Politics.

The supporters of the Trump presidency (and the POTUS himself) along with the supporters of Brexit have all become both applauded and condemned for their Magical Thinking.

Meme wars have raged in the noosphere as one might expect now that the Pandaemonaeon gets into its stride on the back of globalisation.

See this https://pepethefrogfaith.wordpress.com/

And this https://www.ecosophia.net/the-kek-wars-part-two-in-the-shadow-of-the-cathedral/

Note the references to Chaos Magic specifically.

Googling ‘Kek Frog God’ may provide some interesting surprises for those outside the American meme-sphere. In the next meme war we can expect to see far more of this  phenomenon.

I guess a lot depends on whether the applauders or accusers like Trump and/or Brexit, and whether they consider Magical Thinking deluded or effective or, more interestingly - both.

Either way it has worked pleasingly well as a guiding principle in my life.

I recently watched The Darkest Hour in which Churchill rallies Britain to resist a seemingly inevitable domination by Germany. It worked brilliantly at the time, (although I note that Germany has recently acquired the Skoda works for which it invaded Czechoslovakia and the remains of British Steel have just fallen to Krupp. Plus, they effectively own Greece now, and evidently still quietly believe themselves at least the economic master race).

British foreign policy has for centuries had two guiding principles - self-preservation and the prevention of hegemony developing in Europe. Let us hope that Brexit hastens the breakup of the EU. 

In its most ideal and heroic form Magical Thinking says, ‘We Can and We Will’ despite common sense, ‘the facts’, all evidence to the contrary, and all received wisdom and expert opinion: - because nothing has ultimate truth and anything remains possible. (NUTARP! as we say in Chaos Magic).

As Sturgeon’s Law states - Ninety percent of everything (and everyone?) consists of Bullshit. History consists of a ghastly mess of miscalculations, unintended consequences, and unanticipated events punctuated by the rare appearance of ideas that prove effective.

Humanity has a surfeit of experts, but no experts on the future. Yet I believe Britain could have a better future outside of a stifling, bureaucratic, synarchist, undemocratic EU, and that therefore it should try - whatever the short-term costs; and that Trump has not actually DONE anything catastrophically stupid yet despite the negotiable braggadocio, therefore we should wait and see if his alarming and refreshing new approach works. 

Humanity advances by challenging its beliefs about its limitations.

We Can halt global warming by going over to renewable energy sources.

We Can stabilise the human population at sustainable levels without genocide.

We Can stop economic ‘growth’ without reducing our quality of life.

We just need to summon the belief that we both Can and Will accomplish these things. The Knights of Chaos may sally forth again in support of any of the three above - if we can agree on strategy and tactics.

Rebel Physics. What underlies the large number coincidences of the cosmos? More than mere human numerology methinks.

Just as the current Apophenia 2 draws towards a close She gifted me another Yog-Sothianan insight:

The mass of individual matter particles* in the universe and their total number AND the ratio of the Planck scale to the Cosmological scale mutually define each other.

Herewith the calculation in orders of magnitude terms in SI units: -

1) From Hypersphere Cosmology; the mass, length (antipode), energy, and time (temporal horizon) of the universe all have the same multiple (the Ubiquity Constant U) of the Planck mass, length, energy and time respectively. The Ubiquity Constant has a value of 10⁶⁰. This huge dimensionless number acts as the magic number from which all quantum-cosmic ‘coincidences’ follow.

2) From Beckenstein-Hawking; The information deficit of the universe as a gravitationally closed system has the same order of magnitude as the Ubiquity Constant U, in terms of bits per Planck volume which results in a deficit of the cube root of Ubiquity (10²⁰) per Planck length. Thus, the universe has an effective grain size or pixilation at 10²⁰ times more than the Planck length, rather than at the Planck length itself. and this does indeed seem reflected in the ‘size’ or wavelength of stable baryons*. Few lengths below this seem to have any real physical meaning.

3) The measured mass of baryons* comes out as 10²⁰ times less than the Planck mass, yet this figure inserted into the DeBroglie equation of wavelength = Planck’s constant / mass x lightspeed also yields a figure for baryon wavelength commensurate with the above.

4) From 1), 2), and 3) the total number of baryons* (matter particles) in the universe comes out at 10⁸⁰, or U^4/3, a number which fits comfortably with estimates derived from the number of stars and galaxies in the universe and their masses.

5) That the above relationships seem exact now, suggests that either we live in a very atypical epoch of the universe or, more likely, that the expanding universe hypothesis remains a faulty interpretation of observational data which we could better explain using hypersphere cosmology.   

*Note that ‘matter particles’ or ‘baryons’ here means either proton-electron pairs or neutrons (which have the same mass, and which can interconvert) and which in a ratio of about 3 to 1 account for virtually all the mass of the universe at 10⁶⁰ Planck masses, (10⁵² kg.)

Thus we can not only see the entire universe in a grain of sand, we can also see it in a single subatomic particle of matter.

Sculpture.

Herewith a midsummer sculpture for the gardens, a vertical sundial calibrated in situ for a south facing wall.  Turdcrete over steel wire with a figure of Time/The Grim Reaper done in plumber’s tin solder with blowtorch and soldering iron. Photographed on Solstic morning, and hour and a half before Midday GMT and subsequent mounting high on wall. Sorry photo on side.

Provisionally titled ‘Life’s too Short to be an Asshole’.

Magic.

On Arcanorium College the Apophenia 2 course winds down after Her birthday in May and we examine the inspirations received.

Currently we discuss Lionel Snell’s book ‘My Years of Magical Thinking’, probably the most deep and profound work of Magical Philosophy ever published, alongside Matthew Hutson’s ‘The Seven Laws of Magical Thinking’ a rather slimmer and more populist book for civilians which nevertheless raises some interesting questions.

A new course/extended discussion and practical on the topic of EXPERIMENTAL BELIEF may follow shortly.

Physics.

The Standard Model (Lambda CDM) of Cosmology posits a big bang and states that the nature of reality prior to this ‘is’ unknowable and beyond the bounds of scientific inquiry.

The Standard Copenhagen Interpretation of Quantum Physics states that the nature of the underlying reality ‘is’ unknowable and beyond the bounds of scientific inquiry.

What a come on! Surely, as wizards we can do better than this.

I suspect that in both cases orthodox science has made some erroneous assumptions about Time.

In the cosmological domain the redshift in the wavelength of light from distant galaxies became misinterpreted as an expansion of space, and manifold nonsense has resulted, such as cosmic singularity, cosmic inflation, big bang, dark matter and dark energy - all forms of phlogiston required to patch up the discrepancies between the resulting mistaken theory and actual observations.

If instead theorists had concentrated on the frequency of cosmic light they might have modelled the decrease of frequency (Time rather than length) with cosmic distance in terms of a deceleration arsing from a small positive spacetime curvature A.

Thusly: - f_o / f_e = c – sqrt dA  / c

Where f₀ and f_e mean observed and expected frequency, d means distance and                        A = GM/L² (Gravitational constant times mass of universe over antipode distance squared).

This formula accounts for observed redshifts ((by frequency, (or wavelength if inverted)) without recourse to the hypothesis of a big bang and expanding universe and all the infinities and inconsistencies that this leads to.

In the quantum domain the standard assumption of unidirectional one-dimensional time renders the underlying reality inexplicable. Cramer’s Transactional Interpretation does however show how reversible time can explain interference patterns and entanglement.

All the basic equations of physics except for the second law of thermodynamics exhibit a potential time reversibility yet we do not often observe it simply because two-body collisions remain much more likely than three-body collisions and collisions involving even more bodies than that become fantastically unlikely, so stuff basically tends to break, and entropy creates an apparent arrow to time.

The curious wave-particle duality of both energy and matter quanta makes very little sense in a 3D space and 1D time manifold.

However, the transverse wave behaviour of quanta becomes easier to understand if we model it as a rotation of an otherwise unobserved vector that lies in a plane orthogonal to time as we measure it. If a plane of ‘imaginary’ time lies orthogonal to measured time it can account for various of the wavelike features of quanta, quantum superposition, and the apparent probabilistic and indeterminate behaviour of quanta. Imaginary time would act as a kind of pseudospace out of which particle like behaviour decoheres at measurement/wave function collapse.

A symmetrical hyperspherical 3D Time – 3D Space manifold might well explain the deep physics of this universe, and some of the curious phenomena of magic as well.

Flat Universe?

Ah, the Scottish Highlands in spring, what a delight to see the still snow-capped Cairngorms, the sun kissed daffodils around the low roads, and my second granddaughter for the first time. What a surprise also to see The Flat Earth shop in Inverness and all the flat earth graffiti on the surrounding road signs; some people up there seem to take this as seriously as the Loch Ness Monster, and Dour Protestant sects by the bucket load.

Whilst I admire eccentricity and non-conformity, Flat-Earthism does seem rather vulnerable to immediate falsification. You may laugh but remember that almost the entire scientific community still subscribes to Flat Universe theory – the idea that exact Euclidian geometry applies to the whole universe thus giving it an overall zero curvature, a big bang beginning and a catastrophic ending.

You might think that the pervasive superstition of an explosively expanding universe suggests a negative curvature but by miraculous coincidence all the supposed mass within it supplies a positive curvature (gravity) just capable of arresting the supposed expansion given infinite time.

In centuries to come our descendants will laugh at Flat-Universism as heartily as we now laugh at Flat-Earthism. The cracks of its impending falsification have already appeared where you would most expect them – in the ‘crank’ scientific papers written by people such as myself.

The hypothesis of Hypersphere Cosmology for example: -

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

shows that the universe has an observable positive curvature which we can see in the residual Pioneer deceleration, the retardation of the frequency of light when it traverses cosmic distances, and the diminution of type 1A supernovae luminosity due to cosmic hyperspherical lensing. Moreover, the hypothesis also explains the anomalous galactic rotation curves without dark matter and provides the only scenario in which Mach’s Principle of the origin of inertial mass can apply.

http://vixra.org/abs/1710.0066

All these parts of the hypothesis come with rigorous supporting mathematics.

Does any of this matter to us tiny humans on this quaint little planet in the suburbs of one unexceptional galaxy among billions?

Well it matters intensely to me because our views of the universe underlie our metaphysics and philosophies and religions and theories of magic, and thus what we believe about reality and thus how we live.

The big bang hypothesis with its big crunch or entropic fade-out ending seems a horrible sort of monotheistic style apocalyptic scenario from which humanity can never escape except to the imaginary transcendental realms of some great sky-fairy or other. This doesn’t encourage people to value this life or to look after this planet.

On the other hand, the Hypersphere Universe has no beginning and no ending, it has finite but unbounded extent in space and time – meaning that you can never fall off the ‘edge(s)’ of it in any dimension. Humanity could survive for effectively unlimited time if it proves clever enough to move to fresh habitats as stellar and galactic events render old ones unusable. Plus, the universe having effectively unlimited age will most certainly contain intelligences far older than our own that may eventually decide that we have become worth communicating with.

Meanwhile the extended Apophenia working on Arcanorium College continues to produce a splendid burst of inspiration and creativity in many fields.

For me it has led to the evolution of the structure of Square Rigger Chess as a sort of distraction activity (soon to appear on the games pages) whilst making some progress with the Quantum Hypersphere hypothesis. It has become clear that the phenomena of individual quanta depend on the phenomenon of the entire universe; as Hermes Trismegistus quipped – As Above, So Below.

Imagine a perfectly spherical planet with no land, just an entire surface of water. Drop a rock into it and circular waves spread out, eventually these waves will converge on the other side of the planet and get higher as the circles get smaller, finally producing a spike in the water as the inverse of the hole in the water that the rock made.

Three dimensional spherical waves in a hypersphere will do something analogous in a hypersphere. An antiparticle will appear at the antipode.

That an antiparticle appears at the antipode may seem a little odd. However, consider this – if you travel to the other side of this planet you end up upside-down with respect to your starting orientation, you have rotated 180 degrees. If instead of simply moving across a slightly curved plane to a terrestrial antipode, a particle moved right across/around the curved hyperspherical universe it would become rotated through all dimensions of space and time to become its mirror image antiparticle.   

This all seems to fit in with Milo Woolf's ideas on particles as spherical standing waves, the transactional interpretation of quantum mechanics, and the hypersphere cosmology idea of antipodal particles having opposite matter/antimatter sign.

De Broglie hypothesised that matter quanta have the wave/particle duality that energy quanta exhibit, and indeed we can now demonstrate quantum entanglement, superposition, and tunnelling with matter quanta such as electrons. As the transactional interpretation of quantum mechanics seems the only one capable of providing a physical-principle model for these phenomena then presumably the phenomenon of moving matter particles must also arise as a transaction process in which advanced waves move backwards in time.

Thus, the wave function of any quantum stretches all the way around the universe to its antipode point at about 14 billion light years away.

So, a photon, an electron, a proton, a ball bearing, this planet, you and I, all consist of interreference patterns that manifest as particles out of wave functions that extend right around the entire universe.

Om.  

Springblog

I feel thrilled to announce the spring arrival of a second Granddaughter. Mother, baby, and husband all doing great, they put this down to the hypno-birthing techniques they used, plus I guess an oat-fed hardy Highland lifestyle helps.

Life up there certainly has some big upsides, you can wander around the miniature city of Inverness without having to watch your back, and random people will strike up pleasant conversations with you and none of them seem mad or demand anything of you. Plus, you can actually observe people walking around or sitting down without the aid of mobile phones.

In a further celebration of spring all three ponds have started to fill with amphibia, frogs and toads in the mature ones and just frogs so far in the new one. Just in time for the spring equinox I finished and hung Sol Invictus on a south facing wall and readied the Moon for a propitious hanging date. These consist of ‘turdcrete’ (sheepswool and bracken compost with Portland cement) over steel wire frames, acrylic finish.

Have you noticed the appalling deterioration of political and social debate in the years since the development of the internet and social media? Debate seems to have descended into the hurling of insults, recycled soundbites and abstract memes. The words ‘fascist’ or 'phobic' seem to have become items of punctuation, and applied liberally to anyone the speaker fears to even enter debate with and would therefore rather no-platform to preserve the safe space inside their head which has become so fragile due to the abandonment of critical thinking. It seems that in this age of mass-alienation and too much information, so many people seek the identity and solace of niche-herd-minds and preformed opinions.

Perhaps that constitutes the secular substitute for religion these days. We used to value the principle of trying to see the others’ point of view, at least in secular matters, but if opinion and identity become a religion, that option goes.

Correspondents inform me that even the esoteric social media platforms have degenerated into factional invective these days.

As an antidote to all this Arcanorium College proudly announces that we will shortly conduct a Philosophy of Magic course, a leisurely debate over some months.

We shall conduct this as always, as men and women of letters.

My IT guy has eliminated the cryptocurrency mining franchise which had apparently taken up residence on this site and also he has upgraded the template, so bear with me whilst I learn it anew.

Firstly, wow, what a device, see this link  https;//ldrt.ch/tks127

And now, a random rambling cornucopia of bits upon reaching pensionable age: -

Old age doesn’t seem so bad when you consider the alternative, over the hill seems preferable to under it.

I gazed upon the star Aldebaran having discovered that due to its distance at 65 light years, the light I perceived (and hence became quantum entangled with) set off on my zeroth birthday. I hope that I have not inadvertently just invented yet another useless form of natal astrology.

Nevertheless, I do hope against all sense and reason to survive to see my Uranus return (84 years), much remains to do, sorting the cosmology problem took 20 years, quantum hyperspheres remain a daunting quest. We still lack a tight theory of the magical link.

A festive interlude in the Scottish Highlands visiting the expanding clan proved a delight. A six-mile hike to the top of Plodda falls through icy and beautiful terrain culminated in a magnificent view and a splendid experience of vertigo, and afterwards so as not to show weakness in front of the Scots we did a sub-zero outdoor barbeque.

Fort George on the Moray Firth provides examples of one of the largest Georgian artillery fortress in the world and the bizarre bonkers-ness of regimental life. It even has a cemetery for regimental mascots and officers dogs. Highland battledress seems designed to convince any enemy of the dangerous madness of the wearer. The fortress seemed awesomely overbuilt just to supress any unlikely further Jacobite uprisings after Culloden, perhaps it also serves to interdict the passage of monsters to the Ness. Thirteen-inch bore mortars seem a bit excessive for use against tartan-clad swordsmen; I think they actually threw depth charges.

A post festive trip to Barcelona brightened up the end of January; we did the inevitable tourist sights. The Modernista Sagrada Familia cathedral looks brilliant from a distance or as a monochrome scale model. Close up however it looks laughably kitsch and tacky. Catholic cathedrals usually have a dignified exterior and reserve all their gaudy sentimental and macabre religious tat for the inside. Unfortunately, here they have put it all over the outside as well, making it look like a castle in a religious Disneyland. Because they have used modern materials it probably will not last a century judging by the deterioration of the Park Gueli structures by the same architect.

The early Picassos impress with their superb draughtsmanship and eclecticism of styles. The late ones suggest a profound diminution of eyesight and mind.

A side pilgrimage to the Salvador Dali theatre/museum/shrine at Figueres proved the high point of the holiday, a day in the dreamscapes of the high priest of Pareidolia; hallucination and imagination and the subconscious running in splendid magnificent riot.

Do I worry about the POTUS? Not much. Politics has always consisted of a shitstorm of spin, misinformation, propaganda, and fake news. Technology has merely accelerated this and made it more obvious. Trump hasn’t actually done anything too terrible yet despite playing a mixture of madman strategy and dumbman strategy that has thoroughly confused his adversaries. We only used to find out about the downsides and clay feet of our glorious leaders long afterwards, now we get it in realtime. At least North Korea and South Korea seem to have made friends at last, loudmouth madman strategy can work you know.

Whilst away I read a copy of Dan Brown’s ‘Origin’, I got for xmas. This lively story revolves around the discovery of a bit of science that could overturn most of the world’s major religions.

I won’t spoil it for you except to say look out for the bits on Chaos and the Chaos symbol itself in the text.

The discovery didn’t turn out as I’d expected from the cosmological hints in the story, nevertheless it certainly would throw a spanner in the works of most creation myths if it pans out.

This led me to muse upon a discovery that would undermine ALL creation stories and myths, including the scientific creation myth, and I realised that we may have it already: -

                           WHAT IF THE UNIVERSE HAS NO ORIGIN?

That probably sounds crazy within almost everyone’s current thought processes, we remain accustomed to phenomena having a beginning and an ending, although they merely change from one state to another, but if we rephrase it as -

                                 WHAT IF REALITY HAS NO ORIGIN?

Then it perhaps becomes easier to contemplate

It lies here -

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

Awaiting confirmation or falsification.

And in other news, asked to explain my aparently incomprehensible political position I came up with this:-

Entropolitics.

Inequality has come in for fashionable criticism recently, but do we really have too much of it or do we not have enough of it?

On one hand many of us spend much of our lives life trying to gain financial, social, and intellectual advantages over our fellow humans and to pass such advantages primarily to our offspring, and secondarily to our tribes of family, friends, and nation. We applaud ambition.

On the other hand, we tend to demand reciprocity from those who achieve wealth and power, and we find satisfaction in forcibly redistributing it through taxes and revolutions.

Yet wealth and power seem like heat in thermodynamics, they only do useful work when unevenly distributed.

Life itself, and lively societies, require entropy gradients.

Temporarily dominant individuals, polities and empires have created or sponsored most of our culture, science, art, religion and magic.

Ancient Egypt, Classical Greece, The Roman & Chinese Empires, The Islamic Empire, Renaissance and post renaissance Europe, The British Empire, The post WW2 American Empire, and now perhaps the New Chinese Empire. (Non – exhaustive list, I just picked some of the big players). A lot of people had, and will have, fun, liberation and enlightenment in building up and in attacking these structures.

Useful work occurs as wealth and power accumulate and then dissipate, as social friction, upheavals, revolution, and war occur.

Inequalities of wealth and power, empires and patronage, and the initiatives to tear such things down, have led to all the advances of our species.

As a Chaoist I do not have to have a set of opinions that conforms to other people’s standards of consistency.

Have you noticed how boring and dull equality gets? Strife seems so much more stimulating.

I reject the EU on the basis that it seeks to create economic and moral uniformity from the Baltic to the Mediterranean and from the Atlantic to the Urals.

Have you heard much interesting news from Denmark, Sweden, Norway or New Zealand recently?

Do you think that redistributive social welfare policies lead to the unnatural survival of feckless fools and apparent failures, and a resulting drop in collective fitness, or a useful broadening of genetic diversity?

Do you think that all cultures, societies, religions, and moral philosophies have equal value?

Alternatively, do you think some cultures, societies, religions, and moral philosophies have outlived their initial usefulness and gone bad and now need destroying?

Yes, I feel simultaneously conservative and radical. Inequality seems worth both striving for and against, depending on context and personal circumstance.

A healthy polity encourages both the accumulation and the dissipation of wealth and power.

Chaos, Discord, Confusion, Bureaucracy, Decadence.

The Zeitgeist revolves, hopefully in an upward spiral. Western civilisation currently seems currently on the cusp between Decadence and a New Chaos.

In the developed world we have sorted out the Discord and Confusion with many revolutions and a massive dose of Bureaucracy only to find that Decadence doesn’t seem all that satisfactory either.

Hail Eris!

Plus Also ::: I may yet collaborate on another book which we shall definitely NOT call '50 Shades of Gnosis'.

This will deal with a huge variety of methods of achieving altered states of mind, belief, and magic. (None of them involving chemognosis because that never lived up to the hype and I never met a wizard who made a success of it.)