The Apophenion: A Chaos Magick Paradigm - Peter J. Carroll 2008

Non-Singularity - Cosmology

Introduction. This chapter seeks to undermine the notion that the universe must contain some kind of ontological singularity or metaphysical catastrophe like an infinity, or a Big Bang beginning, or a Big Crunch ending, or a god to start and finish it. Such things put its existence beyond rational understanding in principle because they introduce a profound self-inconsistency, the physics on which the universe runs breaks down at a space-time singularity and god based explanations usually supply nothing more than an excuse to selectively abandon rational enquiry altogether.

This chapter seeks an Apophenia in the idea that any real quantity has a finite yet sometimes unbounded extent, and that no real quantity can have an infinite value.

Thus it attempts to undermine the whole linear time paradigm of occidental and monotheistic thought which endows the universe with a beginning and perhaps an end.

Instead it posits a universe that consists of a finite and unbounded amount of both space and time and which exists naturally, simply because it exhibits physical and magical self-consistency.

Part 1.

Against Singularity

An erroneous consensus has developed amongst astronomers in recent decades that the universe began about 13 billion years ago with some kind of a big bang. Three lines of evidence have led to this conclusion.

Firstly the light and other electromagnetic radiation from distant galaxies has less than the expected amount of energy when it reaches us. As light invariably travels at the constant light-speed in free space, this energy loss appears as a red-shifting of the light towards the lower energy end of the spectrum. Astronomers interpreted this as evidence that the universe had expanded from a much smaller size in the past and that the expansion of the universe had stretched the light waves out, thus increasing their wavelength and lowering their frequency and energy. At first it seemed that the amount of redshift corresponded roughly to distance, implying a constant rate of expansion or perhaps a rate which had slowed slightly over time due to gravity. More recent observations seemed to suggest that the expansion rate had somehow increased with time. As a logical consequence of this hypothesis it seemed that the entire universe must once have had virtually if not actually zero volume and an infinite or near infinite density. Observations of the redshifts of very far galaxies suggested that they recede from us at velocities approaching light-speed.

The second item of evidence comes from the cosmic microwave background radiation or CMBR. A light and uniform drizzle of microwave radiation comes in from all directions in space, indicating that most of it comes from very deep space beyond our galaxy. Astronomers interpreted this radiation as a remnant from the very hot fireball state in which the early universe supposedly existed. By now the expansion of the universe had supposedly cooled the radiation of the primordial fireball down to weak microwaves.

A third item of evidence depends on a circular argument. The universe appears to consist of about 75% hydrogen and 25% helium with just a tiny smattering of the heavier elements. Now from what we know of the synthesis of helium and the heavier elements in stars from hydrogen, the stars have not had long enough to make all the helium we can observe if the universe started with only hydrogen about 13 billion years ago. Thus astronomers concluded that the primordial fireball itself must have made most of the helium.

Now the big bang theory which developed from these interpretations of observations suffers from very many problems which theorists have attempted to overcome with a variety of theoretical patches, fixes and fudge factors which have created even more problems and inconsistencies.

Herewith a small selection of some of the most serious problems:

Nobody has a convincing explanation of how the entire universe could have got into the absurdly unnatural state of zero size and infinite density in the first place, or even how it could have expanded out of this condition.

Nobody has a convincing explanation for the apparent uniformity of the universe on the very large scale; such uniformity does not seem a likely consequence of a big bang. The cosmic inflation theory attempts to solve this problem by supposing that space itself somehow expanded at virtually infinite speed to create a universe of the size we now observe, or possibly a much larger one, and that the matter and energy expansion followed afterwards. No credible mechanism exists to support this hypothesis.

Nobody has a convincing explanation of why our best theories of gravity contradict the big bang hypothesis. Theorists have attempted to tinker with gravity theory and to introduce extra sources of gravity and anti-gravity rather than question the big bang orthodoxy. Few professional theorists have dared to doubt the big bang hypothesis itself. At the time of writing, such a policy looks like a suicidal career option on a par with taking a professional interest in parapsychology.

It appears that many galaxies do not contain enough matter to explain how they manage to rotate at the speeds we observe without flying apart. Conventional theory favours the idea of so called 'dark matter' to balance the maths. This stuff does not consist of anything even remotely like the stuff that comprises this planet, our star, and us, yet according to theory it should comprise a substantial fraction of the entire universe. Its properties imply that we can never actually get hold of a bucketful of the stuff and test the idea.

A minority conventional theory called MOND, modified Newtonian dynamics, merely adds whatever fudge factor you need to balance the equations, without offering a mechanism.

The apparent acceleration of the apparent expansion of the universe has led theorists to posit the existence of so called 'dark energy'. If it exists, such dark energy must comprise the majority of the energy in the universe. Yet it must have the astonishingly convenient ability to exhibit anti-gravity to force the universe to expand in an accelerating fashion, and simultaneously the ability to exhibit ordinary gravity to make space appear geometrically flat.

Such hypothetical substances as dark matter and dark energy begin to resemble the Phlogiston which medieval theorist invoked to explain why things burned. Set a piece of wood alight and you end up with a much lighter pile of ash at the end. Ergo the wood must contain Phlogiston that appears as fire and accounts for the weight loss.

When some bright spark noticed that the residue from burning metals actually weighed more than the original metal, (we now know that burning metals absorb oxygen), the Phlogiston in metals then got credited with negative weight, whatever that means.

Nevertheless, despite the highly dubious patches and fudges required to keep the big bang theory afloat, the majority of professional cosmologists confidently assert as fact the idea that the universe consists of about 10% ordinary matter, 20% dark matter, and 70% dark energy. Their jobs depend on it.

Cosmologists are seldom right, but never in doubt, as the old saying goes.

However a far simpler explanation exists for the observed galactic red shifts, the CMBR, galactic rotation rates, and helium abundance. It does not involve a big bang, or fudge factors like dark matter, arbitrary adjustments to gravity theory, or dark energy, or an unexplained preliminary inflation of the universe, and absurd initial conditions.

It simply suggests that the universe has a small positive space-time curvature and thus that it exists as a finite and unbounded closed structure (a hypersphere) in both space and time which undergoes a very slow kind of special 'rotation' which prevents it from collapsing. Part 2 of this chapter gives a verbal description of such a structure and Part 3 discuses the philosophical, metaphysical and magical implications of this model. The mathematics which describes it precisely appears in Appendices (ii) and (iii).

Part 2.

The Hyper-Spherical Universe

If nothing can exceed the speed of light, as special relativity asserts and experiment appears to confirm, then any structure with enough gravity to have an orbital velocity of light-speed will function as a 'closed' region of space-time from which nothing can escape. Anything, including light, which attempts to escape, will simply fall back in again or just keep on going round and round forever. The gravity of the structure basically makes space (and time) curve back in on itself in accordance with the theory of general relativity which describes gravity not as a force, but as a curvature in space and time.

Einstein originally thought that the universe consisted of a structure like this, but he had to add a fudge factor which he called the cosmological constant to stop it collapsing in on itself under its own gravity, because it plainly hadn't done so already.

Gödel came up with the idea that the Einstein universe might rotate and thus not collapse, in the same way that the orbital velocity of a planet stops it plunging into its star. However Gödel's model treated the universe as a sphere which would have had an axis of rotation. This would have showed up fairly obviously to astronomers and it didn't. Then the red shift data appeared and the idea of an explosively expanding universe replaced that of a static universe maintained by a mysterious cosmological constant.

A gravitationally closed universe has a positive space-time curvature and the geometry of a hypersphere. Now a hypersphere represents a higher dimensional version of a sphere in the following way. We can consider an ordinary sphere as a two dimensional surface bent round in a third dimension to create a ball, so that the surface no longer has edges. The simplest hypersphere, the so called 3-sphere, consists of a three dimensional volume bent round a fourth dimension to form a structure which has no edges either, it joins up with itself rather than having edges.

To visualise a hyper-sphere consider the possible ways of making a flat map of the earth, they all involve some kind of distortion, but we will have to distort the hypersphere a bit anyway as our visualisation abilities do not work too well in more than 3 dimensions.

You can cut a globe of the world into two hemispheres across the equator and place them next to each other and take a photograph of them. This creates a so-called polar projection that gives a realistic view of the Arctic and the Antarctic but tends to distort the equatorial regions. In such a polar projection, the two circles showing the northern and southern hemispheres normally get placed in contact at some arbitrary point. This reminds us that the now divided equator actually remains in contact with itself at all points, so we could roll one circle around the other to any position to show this. Using this idea we can form a fairly good mental model of a hypersphere. A hypersphere would consist not of two circles in contact but of two spheres in contact, with the proviso that the spheres are actually in contact at every point on their surfaces, which we can represent by continuously rolling the spheres around over each others surfaces. In such a situation nothing can escape the structure. If anything exits the surface of one sphere it immediately enters the other one at the corresponding point on its surface. The division of the hyper-sphere into 2 spheres does not imply any sort of division in reality or any special status accorded to the centre or surface of either sphere. When we cut the world globe into two hemispheres, we can 'cut' it anywhere for representational purposes. We could cut it across the Greenwich meridian and dateline to show an east and west hemisphere if we wanted.

We do not have to centre such projections on the north and south poles. Similarly the centre points of the two representational 'halves' of the hypersphere have no special status, the hypersphere has no centre in the same way that the surface of the earth has no special centre points.

However a hypersphere has a similar property to the surface of an ordinary sphere in that any point in it has a corresponding antipode point which represents the furthest point that you can travel to from the original point until you start coming back towards it from the other direction.

The above description shows the properties of the three dimensional 'surface' of the hypersphere. Technically speaking a hypersphere exists as a four dimensional structure with its 3 dimensional surface embedded in four dimensions, much as an ordinary sphere consists of a two dimensional surface bent round to achieve closure, embedded in a three dimensional space. The fourth dimension of a hypersphere does not have to extend beyond the three dimensional surface. It can consist merely of the curvature of the three dimensional surface which results in the 3D 'surface' having a slightly higher internal volume than it would appear to have if you could look at it from the outside, and assumed that it consisted of a sphere.

Now a hypersphere has several properties which theorists failed to take into account when they discarded it as a model of the universe in favour of an expanding model.

A hypersphere can have a kind of rotation but this consists of something a little more complicated than the simple rotation of an ordinary sphere about an axis, like the north-south axis of our planet. A hypersphere rotation consists of a rotation of the three dimensional surface volume about the radius of curvature, which lies at right angles to all of the three spatial dimensions. We should more properly call such a rotation a 'vorticitation', we cannot easily visualise it, but it corresponds roughly to the idea of a ball of dough kneading itself. In effect every point in the hypersphere changes place with its antipode point and then returns to its original position to complete a single vorticitation. In a universe of this size it would take about 22 billion years, yet it would create a centrifugal effect which exactly balances the centripetal effect of the gravity or positive spatial curvature of the universe. Thus a vorticitating hypersphere can remain stable without collapsing or having to expand.

The combined effect of the centrifugal and centripetal effects in a vorticitating hypersphere would produce a small resistance to linear motion in any direction within the three dimensional space. We have already observed the deceleration of space probes dispatched some years ago to the extremities of the solar system. This so called Pioneer Anomaly or Anderson acceleration has led to much debate and argument among theorists. However if it does represent the positive space-time curvature of a hyperspherical universe then it tells us the exact distance to the antipode (effectively the 'size' of the universe) and also its exact weight, because a simple equation links together these quantities for a structure with an orbital velocity of lightspeed.

The measured value of the Anderson deceleration gives an antipode distance of 11 billion light years, and this represents the greatest separation that any two points can have in a hyperspherical universe

This cosmic deceleration factor arising from the spacetime curvature offers an alternative explanation for redshift, which in a hypersphere results simply from distance, not from a general expansion of the universe.

The geometry of a hypersphere has an additional lensing effect which tends to magnify objects in the vicinity of the halfway to antipode distance and to reduce the apparent size of objects further away. This explains why the redshifts of the type 1A supernovae used as 'standard candles' do not match distance estimates derived from apparent magnitude. This mismatch has led to the erroneous conclusion of an accelerating expansion of the universe, and the hypothesis of dark energy to propel it.

The vorticitation of the hypersphere implies an omni-directional type of rotation in which all widely separated bodies rotate around each other, and this rotational frame adds significantly to orbital velocity at galactic distances by a factor of the square root of distance times the Anderson deceleration. At planetary distances the effect remains negligible, but at galactic distances it allows orbital velocities to have higher than expected values, without dark matter.

A hypersphere has a finite and unbounded extent in space. You cannot get out of it because it has an orbital velocity of lightspeed, and an unachievable escape velocity of the square root of twice lightspeed, yet you can travel around in it as far as you like without encountering any kind of edge or boundary. If the universe consists of a hypersphere then the question of what lies outside of it has no meaning because all of the 3 dimensional space that exists lies within it. Space does not consist of the mere absence of stuff, it consists of the curvature subtended by matter, and where the matter ends, not even space exists, so it has no outside. However a hyperspherical universe will have a spatial horizon, a distance beyond which you cannot see anything, because light from objects near your antipode will become redshifted to oblivion, and the antipode will appear to lie at the extreme of every direction you look in, rather as the south pole of the earth lies in every possible southward direction from the north pole of the earth.

The hypothesis of 3 dimensional time advanced in chapter 5 of course applies to the universe as a whole and the positive spacetime curvature arising from the gravity of the universe would also lead to a universe with finite and unbounded extent in time. Thus although the universe will exhibit a temporal horizon of 11 billion years, nothing in principle prevents something from persisting for longer. Some of the older galactic structures do seem to have an age greater than the temporal horizon, but few of the macroscopic structures in the universe seem likely to survive for such lengths of time.

Stars expand and explode consuming entire planets and heavy neutron stars recycle higher elements back into hydrogen.

Thus the helium abundance does not require a primordial fireball to explain it. The proportion of elements in the universe represents a constant equilibrium.

Light from a distant galaxy that comes towards an observer will become redshifted by the Anderson acceleration. However, light from objects which travels away from the observer will also eventually reach the observer, having passed the antipode and come back again. This light will have travelled more than once round the universe and become profoundly redshifted. Yet it will not completely disappear because the vast tracts of space it passes through contain diffuse clouds of gas and dust which gradually absorb and re-emit the light until it reaches equilibrium with the temperature of the dust and gas in intergalactic space. Absorption and re-emission begins to dominate over the effect of further redshifting as the lights energy drops towards that of the temperature of the intergalactic medium. This residual light then appears to us as the microwave background. It does not represent the cooled afterglow of a cosmic fireball, it merely represents the constant temperature of the universe, which comes in at a rather chilly 2.7 degrees above absolute zero, because it mostly consists of rather cold and fairly empty space.

Part 3

Hyperspherical Metaphysics

Although the hyperspherical universe outlined above has a spatial and temporal horizon beyond which we cannot see; it has no beginning or end. Although both space and time exist as vast closed curved structures, events within this universe do not undergo eternal recurrence. If you sit still for 22 billion years you will in theory return again to the same point in spacetime in this vorticitating structure, but don't expect to find the exact same events occurring there again, because events will have moved on.

The hyperspherical universe hypothesis gives rise to a peculiar inversion of the type of answerable question that we can pose. We can ask and answer the question of why it exists. It exists because it has self-consistency. However we cannot ask or answer the question of how it got that way. We have a strange tendency to regard nothing as somehow more fundamental than something. Yet we have absolutely no reason for this assumption, indeed the evidence all points to the contrary. We never observe anything coming from nothing, everything we observe appears to have come from something else. Structures come and go, but the underlying space, time, mass, and energy merely rearranges itself endlessly. We can observe no mechanism which creates these phenomena, nor any which could lead to their demise, so why do some people persist in imagining that the universe has an origin from some prior state of nothing? I suspect that the whole idea arises from our lamentable capacity to ascribe reality to things that don't exist like 'being' and to privative concepts like 'nothing'.

So does the hypothesis of a vorticitating hypersphere constitute a TOE, or 'theory of everything'? Most definitely not, and it seems that Gödel's Incompleteness Theorem prevents any sort of TOE from existing, because it proves that any system of maths or reasoning must contain assumptions that we cannot derive from the system itself.

It does however provide a more elegant model of the cosmos than that given by the standard big bang. It depends on only four parameters, G, the gravitational constant, c, lightspeed, h, Planck's constant, and A, the curvature parameter. The relationships between these constants define the sizes of particles and associated forces, and the size of the universe itself. (The electroweak and nuclear forces seem to arise from rather complex relationships in rotating 6 dimensional quantised spacetime which require further explication).

However we cannot derive G, c, h, or A from the hypothesis itself, or from each other, we have to measure them. The hypothesis remains incomplete because we cannot tell why these constants have their observed values, although the word 'observed' may in itself provide a clue.

Nothing 'is' true, but the most self-consistent hypotheses have the greatest utility until someone uncovers incompleteness or finds a more fundamental assumption. Chapter 7 explores the possibility that Psi, the psychism in panpsychism, may supply the missing ingredient.

Part 4.

The Map,

the Journey

and the Meaning

'The dimensionality of the map one uses depends upon the journey being undertaken' - Waldo Thompson.¹⁸

Flat Earth theory serves well enough for a trip from the cave to the water hole and back, and a third dimension going up into the sky and down underground serves to accommodate gods and devils.

A lot of people still think like that, believe it or not.

Spherical Earth theory serves well enough for trips to other continents and gives some intimation of the great space beyond. The gods and demons begin to retreat into unseen dimensions.

Flat Space theory serves well enough for trips around the solar system if you acknowledge gravity as a force. Those pictures of the Earth from the Moon were worth a thousand words about what it means to live on a planet in a space of almost indescribable enormity. The gods and demons have no place to hide but in the hearts of humans. Curved Spacetime theory leads to an apocalyptic universe with a beginning and an end, ruled either by blind chance or an absentee landlord who lives elsewhere. The geometry of this map effectively prevents us from ever travelling far in the territory.

Vorticitating Hyperspherical Spacetime has no beginning or ending but its finite and unbounded extent does not render it incomprehensibly infinite in space either. The chance which rules it does not act completely blindly because 'mind' forms an integral part of its function. Welcome to the participatory universe, the geometry of this map permits magic and invites us to become apprentice gods.

I also suspect that this map will also somehow allow us to take trips right round the territory eventually.

A Chao-Panpsychic Tree of Life.

Herewith some arbitrarily selected steps on the way.

From the perspective of level 7 look down for shamanism and science, look up for religion and mysticism, and for magic look in all directions, nobody knows where most of the arrows go.

Level 0. Some of the fundamentals.

Level 1. Atoms, matter self-organises.

Level 2. Unicellular life, an Amoeba, our GreatGrandparent.

Level 3. Invertebrates. Lord Cthulhu presides. Life gets nasty.

Level 4. Vertebrates. Still nasty, but quicker and a bit smarter.

Level 5. Reptiles. Out of the water, but still in our hindbrain.

Level 6. Mammals & Birds. Neat tricks, they can go everywhere.

Level 7. Us. Still half ape and part crocodile, but dreaming of improvements.

Level 8. Angels and gods. Our dreams of improvement, mostly foolish.

Level 9. Aliens, barely imaginable advanced versions of ourselves.

Level 10. Unimaginably advanced forms of life.

Level 11. Psi. Cosmic Panpsychism.

The Kabbalist may prefer to view the tree as top down; the Scientist may prefer to view it as bottom up, the Panpsychist reserves judgement.