C - AT = 0 (Equation 6)
The Anderson acceleration boosts orbital velocities according to the following equation:
(Equation 7)
This makes negligible differences at planetary distances, but at galactic distances it makes significant differences, and it obviates the need for arbitrarily modified gravity theories or dark matter.
Part 4. Closed Time Curves.
Gödel's rotating universe idea became discarded as unphysical for two reasons. Firstly no axis of rotation seemed observable. However in a hypersphere the axis lies at right angles to 3d space and remains unobservable except as curvature.
Secondly the Gödel universe contains closed time curves and anything travelling around the universe at lightspeed would in theory eventually catch up with its own past, in the sense that it would arrive back just as it began to set off.
In the vorticitating hyperspherical universe exactly this happens, but it does not create a causality problem, rather it solves the problem of causality by making everything the cause of everything. However no form of radiation or matter could in practise survive the 22 billion year trip and expect to arrive in the same form it departed in.
Part 5. Hyperspherical Particles.
Equation 3, for the angular velocity of a hypersphere,
contains a further surprise.
It reduces to , and substituting , to find the frequency f, and then substituting yields:
(Equation 8)
Now if we identify L with wavelength then this equation also represents the basic unit of fermion particle spin, where one half of frequency times wavelength equals lightspeed. This also explains why fermions have to rotate through 720 rather than 360 degrees to restore their original orientation.
Thus it seems that fundamental particles consist of vorticitating hyperspheres as well. This seems inevitable if they have the rotational freedom described by HD8.
Thus Equation 3 unites the Microcosm and the Macrocosm.
I suspect that Hermes Trismegistus would have appreciated that.
I suspect that the Sufis would also appreciate confirmation that everything spins, including the universe itself.
* * *
Appendix IV
The Shape of the Universe
If you live in a hyperspherical universe with a positive space-time curvature but you assume that you live in a flat universe instead, then you will run into strange problems. You will basically end up with worse versions of the problems of horizons and edges that arise if you persist in believing in a flat earth.
A non-infinite universe must have a definite shape and size, but the finite and unbounded hypersphere or 3-sphere which the universe probably consists of does not easily submit to visualisation unless we remove one of the spatial dimensions for illustrative purposes.
The polar type projection mentioned in chapter 6 results from cutting the hypersphere into two hemi-hyperspheres which we can represent as spheres shown by circles in Figure 1.
These two circles represent spheres whose perimeters contact each other at every point on their surfaces. We can imagine this by allowing the spheres to roll freely around each other.
Position A represents an observer in a hypersphere where we have chosen slice it into two hemi-hyperspheres to position the observer in the centre of one of them. We could have cut it anywhere for illustrative purposes, a hypersphere contains no special positions in reality.
Now an observer at position A can set off in any direction and eventually reach position B, an antipode point which represents the furthest distance you can travel from A without starting to return towards it. All straight-line routes from A lead to B, in much the same way that all straight line trips from the North Pole of the earth lead to the South Pole. See figure 2.
In a hypersphere a straight line route, the shortest distance between two points in 3-dimensional space, has to follow the gravitationally induced curvature of the universe itself. Light also has to follow such routes, which we call geodesics.
Now we always construct an image as though light had travelled to us in a straight line. A lens or mirror actually bends the path of light, but because we construct images on the basis of the direction in which light approaches us, objects appear magnified or diminished by lenses or repositioned by mirrors.
When we look out into the cosmos we assume that light has come towards us in straight lines and that the apparent position of objects represents their actual positions.
This works reasonably well for short distances but at cosmic distances the curvature of space-time itself acts like a gigantic lens.
If we assume flat un-curved space then we can represent that by un-rolling the whole of one of the hemi-hyperspheres around the other. See figure 3. Here the antipode point of an observer at A has become spread out right round the horizon. This corresponds to the South Pole of the earth lying in every possible direction from the North Pole. If this planet had such an enormous density that it bent the paths of light around its surface, we would see something like this.
Figure 4 shows what happens to lines of sight in a hypersphere, they curve inwards towards the halfway to antipode distance, and then diverge towards the antipode, from the perspective of an observer who assumes flat space.
Thus, as Figure 5 shows, objects around the halfway to antipode distance will appear magnified whilst objects further away than that will appear diminished, because observers assume that they see in straight lines in un-curved space.
Now light travelling down those geodesics towards an observer will become redshifted to lower energies, and if the observer assumes a flat spacetime, this redshift will become interpreted as an expansion of the universe. However because hypespherical spacetime acts as a giant lens, the observer will notice a mismatch between the apparent magnitudes of objects at various distances and their apparent recession velocities calculated from redshift. High redshift objects will appear fainter, and thus apparently further away than they ought to. Thus our befuddled observer may conclude that not only does the universe expand, but that its expansion rate has speeded up during the expansion.
Of course neither of these things has actually occurred. It just looks like that because we inhabit a finite and unbounded universe of constant size whose curvature distorts what we can see.
* * *
Appendix V
Apophenia's Birthday
Part 1. Theosynthesis and syncretism.
A Mage may gift the world with the naming of a god.
In simpler times, in aeons past, Mages realised god forms corresponding to the basic impulses of love and war, sex and death, fear of the wild-wood, desire for wealth and power, and so on. They also realised other gods to encapsulate the 'souls' of cities or tribes and the lesser functions of the main gods.
In these more complex times we have need of other gods as well, to complete the occult pantheon.
Deo Duce, Samuel MacGregor Mathers, gave us the Holy Guardian Angel concept, which he presented in his Grimoire, based on fragments attributed to Abramelin the Mage. It represents his final understanding of the Higher-Self, Secret Chiefs principle.
Therion, Aleister Crowley, gave us the Aiwass-Horus-True-Will god form in his Book of the Law. It represents his final understanding of The Beast Within; in all its glory and horror, which lurks beneath the veneer of civilisation.
Zos, Austin Spare, gave us Kia, or at least many think he did, for he wrote in riddles.
It appears to resume his final understanding of the panpsychism underlying all phenomena and represents the basic omnivorous chaotic 'life force' beneath the self-image.
Stokastikos, the author, now offers Apophenia, a goddess to embody the occult style of thought itself, which seeks out the hidden connections between seemingly unconnected phenomena, and the strange meanings and inspirations that these connections may bring.
Each of these gods appears to have stalked its priests throughout life as a sort of shadow-like genie until it finally identified itself
and phenomenised.
The author developed an involuntarily hyperactive imagination from an early age, and whiled away his schooldays taking fountain pens on epic interstellar voyages, whilst broadcasting telepathic reports of earth news for the benefit of any passing aliens. Pencil sharpeners became models for vast temples to nameless gods in Amazonian jungles.
Academic performance rarely rose above the avoidance of punishment level.
In adolescence a marked tendency for contrarian and ornery thought developed. Everything seemed questionable and dubious except the exercise of thought and imagination itself. Forbidden, discarded, disgraced, and speculative ideas became particularly attractive and fascinating.
In adulthood, daydreaming became a full time occupation with work breaks fitted in as an afterthought. Well one has to eat and provide for others.
The author still disdains to drive powered vehicles; the scenery just seems to set off too many tangential lines of thought and too many mild hallucinations for safety at speed.
Yes, I have always had Apophenia, or rather She has had me. I didn't even know she had a name until the word came to my attention—So why do I commend Apophenia to my magician readership?
(I can hardly imagine a civilian having read this far.)
Well, since the Eighteenth Century Enlightenment the human enterprise has become increasingly ideas driven. The sum total of ideas increases exponentially nowadays, doubling perhaps every five years or so, and nobody can hope to keep track of all of it. The problems that humanity faces from the application of many of these ideas also seem to increase exponentially, but we cannot turn back now, we need even more ideas to solve the problems that our ideas have already created.
However we do need ideas of a different kind. We need to develop a more holistic view of how phenomena connect with each other. We need to develop an ecology of ideas to see how they fit together, otherwise our lives will become a cacophony of disconnected and largely meaningless experiences whose pursuit will wreck this planet's environment.
We have experts and specialists for everything now, but knowledge as a whole becomes steadily more fragmented and our identities and societies follow suit.
We need Synthesists, Polymaths, Inter-disciplinarians, and Visionaries, we need Apopheniacs of all varieties - her kind of people.
Klaus Conrad coined the word Apophenia in 1958, and defined it as the "unmotivated seeing of connections" accompanied by a "specific experience of an abnormal meaningfulness".
However the full extent of the 'abnormal meaningfulness' did not become apparent until the spring of 2005.
Apophenia phenomenised as a deity in cyberspace on May 26, 2005 at 11.59.46 AM. No previously manifesting deity has had such an accurately recorded time of birth, although Mithras appeared on December 25th, circum 2nd century BC, but some other religion eventually hijacked that date.
The nativity occurred during a transatlantic exchange between the magicians Corlian and Stokastikos and the priestess Dalryada, on the Maybelogic Academy. It happened during an Augoides discussion in the first Internet course on Chaos Magic.
(The author particularly wishes to also thank the very excellent online Maybelogic Academy itself that made this event possible, and Ratatosk the Squirrel of Discord, the technomancer who recovered the data.)
The text of the exchange follows: -
* * *
Part 2.
A Surprise Birthday
Corlian, May 26, 2005, 18:25:42 GMT
"Concerning insanity, and I intend this question for everyone — Does apophenia or pareidolia exist? Do they play the role of myth or threat? Even if patterns lie within everything, can we make a mistake by misdiagnosing a pattern, or does the pattern imply/require that initial misdiagnosis?"
Stokastikos, May 26, 2005, 18:59:46 GMT
(Having spent the last 20 minutes looking up the word Apophenia on Wikipedia, and undergoing a major epiphany)
"Apophenia, Apophenia, APOPHENIA!
A concept in a word,
A word sonorous enough to name a Goddess,
Yes I most certainly feel we need her in a Chaoist pantheon.
Thank you, Pete."
Dalryada, May 26, 2005, 19:23:41 GMT
"— Personally, I'm just thrilled that we've all — scant minutes ago — witnessed the birth of a GODDESS."
May 26 makes Apophenia a Gemini. Subsequent discussions amongst the visionaries of Arcanorium College reveal that Pareidolia must share the same birthday, as her twin. As more of a magician and scientist than a priest or artist I naturally earthed the Apophenic aspect of the twin current. I concluded that whilst Apophenia could bring the Universe in a grain of sand to our attention, Pareidolia merely distracts us with the face of the Virgin Mary in a pavement pizza. Chaos theologists then pointed out the critical importance of Pareidolia in art and mystical religion.
Salvador Dali and whosoever wrote the Book of Revelations must rank as high priests of Pareidolia.
I leave it to the magician-artists and neopantheist-mystics to reveal her formal invocations.
* * *
Epilogue
The example Chaos Magic Paradigm presented in the preceding chapters represents a distillation of ideas and evidence available at the time of writing and summates the last decade of my researches.
The evidence suggests to me that we inhabit a quantum-panpsychic universe consisting of a vorticitating hypersphere, that has finite and unbounded extent in both space and time, and that has equal spatial and temporal dimensionality.
The hyperspherical vorticitation of the universe leads to three dimensional time and this provides an explanation for both the strange behaviour of the underlying quantum realm and the occasional appearance of seemingly magical effects in the macroscopic world.
The statistical effects of random quantum behaviour create a semblance of causality in the macroscopic realm which disguises the underlying chaos but 'Magic' basically structures the universe and keeps it functioning, we participate inadvertently and panpsychically in this process.
Yet we can participate directly by deliberate acts of magic, and it works often enough to justify the effort.
The geometry of the vorticitating hypersphere permits magic and invites us to become apprentice gods.
We have worlds within us. Beneath the veneer of the everyday self we have multiple minds. Thus the Neopantheist style of Mythos belief better reflect our psyche than the Logos style of belief.
The retroactive effects of panpsychism may well explain the general features of this participatory universe.
However I have apophenia, and others may see things differently, we seem to have a lot of alternative realities kicking around these days.
Lastly, some Chaoists may feel uneasy with the idea of a six-dimensional universe. I should perhaps point out that the hidden curvature dimensions of space and time, do in a way constitute another 2 dimensions, each having one pi-th the size of the observable ones.
So that makes a reassuring eight.
* * *
Notes,
References,
and Bibliography
0) Stochastic, means relating to, or characterised by conjecture and randomness. In a stochastic process, non-deterministic behaviour means that a state does not fully determine its next state. Etymology: Greek stochastikos skilful in aiming, from stochazesthai to aim at, guess at, from stochos target.
1) Illuminates of Thanateros. www.iot.org.uk/pages chaosmagic.html
2) Arcanorium College www.arcanoriumcollege.com
3) Alfred North Whitehead. Philosopher and Metaphysician. 1861-1947.
4) David Chalmers. The Conscious Mind: In Search of a Fundamental Theory (1996). Oxford University Press.
5) Nicholas Humphrey in What We Believe by Cannot Prove., Edited by John Brockman. The Free Press.
6) Chalmers, see 4.
7) The User Illusion: Cutting Consciousness Down to Size. by Tor Norretranders Penguin 1999
8) Multimi
nd: A New Way of Looking at Human Behavior by Robert E. Ornstein. Publisher: Ishk 2003
9) Adapted from S.S.O.T.B.M.E. Sex Secrets Of The Black Magicians Exposed, An essay on magic. By Ramsey Dukes. Pub, The Mouse That Spins.
10) Liber Kaos, by Peter J Carroll. Pub, Weiser 1992. See Aeonics chapter.
11) Penrose - The Road to Reality: A Complete Guide to the Laws of the Universe. Vintage Books 2006
12) The Copenhagen Interpretation of Bohr and Heisenberg. Circum 1927. Physics concerns what we can say about nature, it cannot tell us what it actually 'is'.
13) Hidden Variable Interpretation. De Broglie ~ 1927, extended by Bohm ~ 1952. This preserves determinism but locality fails, information travels faster than light.
14) An Overview of the Transactional Interpretation by John Cramer. International Journal of Theoretical Physics 27, 227 (1988) A Farewell to Copenhagen?, by John Cramer. Analog, December 2005.
15) A Brief History of Time: From the Big Bang to Black Holes By Stephen W. Hawking. Published 1988.Bantam
16) Liber Null & Psychonaut by Peter J Carroll. Pub, Weiser 1987. See Gnosis section.
17) See10. Part 2, The Psychonomicon, sleight of mind.
18) Waldo Thompson. www.http://hdcity.com/cosmos
19) The Trouble With Physics: The Rise of String Theory, The Fall of a Science, and What Comes Next by Lee Smolin. Mariner Books 2007
20) Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law by Peter Woit. Mariner Books 2007
21) Principia Discordia - Malaclypse the Younger
Further reading.
Authors Website.www.specularium.org
Uncle Ramsey's little Book of Demons. By Ramsey Dukes. Aeon Books 2005.
The End.
* * *
Mandrake
'Books you don't see everyday'
Apophenion Page 12