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Wednesday, 28 January 2015 15:36

Review and Philosophy.

Dave Lee writes his long awaited and very thorough Review of Epoch

Thanks Dave.

And now for some philosophical musings.

The Philosophical Implications of Hypersphere Cosmology.

Philosophers have long wondered whether the Universe has finite or potentially infinite or actually infinite extension in space and in time.

In the case of finite extension, the question has naturally arisen of what lies beyond it, or what, if anything, ‘contains’ the Universe.

Philosophers have generally regarded space as a Privative Concept rather than a positive concept, and considered space to consist of the absence of things, a nothingness which can accommodate the presence of various phenomena and objects.

Thus a spatially finite universe could, for some philosophers, simply exist within an unlimited space of pure nothingness, but unlimited nothingness means very little except perhaps for the potential for events to happen there.

A Universe consisting of an infinite amount of phenomena and objects spread over an equally infinite amount of space seems a tricky concept. We can say it, but we cannot really visualise it, and many would argue that the concept of infinity can have no physical correlate and that the concept only arises when we take the mistaken course of dividing by zero, or by assuming infinite divisibility, or of assuming that some other quantity has an infinite value. Yet if any quantity has an infinite value then all quantities must have an infinite value. A truly infinite universe would presumably contain an infinite number of stars, an infinite number of earth like planets and an infinite number of creatures including an infinite number of creatures exactly the same as each individual one of us, and an ‘equally’ infinite number of near copies.

Philosophers have also long wondered whether the universe has a finite or a potentially infinite or an actually infinite extension in time, and some have wondered if time itself might have some vast eternal circularity to it, or even to have a purely illusory nature.

Time can to some extent have the appearance of a Privative Concept like empty space, an absence or nothingness which awaits events to fill it up.

The nature of time becomes mysterious in proportion to the amount of thinking devoted to it, yet for any observer, events do seem to have a sequence, some things happen before and some things happen after, that much seems unarguable, and from it we abstract the idea that some form of cause and effect, with the cause preceding the effect, often applies. Even if some observers disagree with others about the order, and some effects appear random, or occasionally retroactive, or magical and occult, the universe broadly seems to go through sequences of events in time, everything obviously doesn’t happen simultaneously.

We can only measure time by movement and change. Potentially infinite time or actually infinite time only has any meaning if some sort of movement or change exists to delineate it.

If absolutely everything in the entire universe stopped moving, right down to the subatomic level, and then started moving again, ‘the amount of time for which it stopped moving’ would remain undetectable and without any effect whatsoever, it would have no reality.

Despite that most of our measures of time have an element of circularity about them; the cycles of night and day, the days of the year, the seemingly endless human cycles of birth and death, the movements of clocks and ultimately the vibrations of atoms in our most reliable timekeeping devices; we also have linear views of time in which many things have a beginning and an end. Even a clock does not exhibit perpetual eternal recurrence; it requires assembly and it will eventually break.

Most monotheist and some pagan religions view the world in terms of a linear timeframe with  deities initiating beginning, a middle, and some sort of apocalyptic and/or transcendental ending, and of course most of them regard the universe as limited in space, often vastly more limited than even the simplest astronomical observations now suggest.

The Privative views of space and time do not now seem sustainable since the advent of General Relativity.

 Newton considered that space provided some sort of fixed absolute immutable void in which objects could exist and that time provided some sort of constant immutable flow in which objects could change. However, most crucially, the objects within space and time could did not affect the space and time.

‘Absolute space, in its own nature, without regard to anything external, remains always similar and immovable.’


‘Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external,’

Einstein’s General Relativity however shows us that the presence of any object; mass or energy, does profoundly affect the properties of space and time. We can no longer consider space and time as voids which can contain events. Space and time have a structure which depends on the presence of mass and energy.

Einstein realised that: - ‘Matter (and energy) tells spacetime how to curve, and curved spacetime tells matter (and energy) how to move.’

Thus gravity does not exist as a ‘force’. Mass and energy give rise to curved spacetime, (that we commonly recognise as gravity) and conversely, spacetime curvature gives rise to mass and energy. None of these phenomena exists independently of the others.

Truly empty space does not exist, it always has some kind of curvature or gravity in it, and the rate at which time ‘flows’ depends on the curvature also.

Einstein’s General Relativity modifies the Newtonian model of gravity under conditions of strong gravity; the Newtonian model remains valid as an approximation where the gravity remains fairly weak. Hypersphere theory modifies General Relativity for the conditions of very strong gravity where the spacetime curvature distorts Euclidian spacetime so much that it adopts a hyperspherical configuration which rotates. This occurs on the scale of the universe itself, almost certainly inside black holes, and rather surprisingly perhaps, in fundamental particles. Hypersphere theory also suggests that the geometry of time matches that of space, and that time has three dimensions rather than one.

For any three dimensional body of roughly uniform density the spacetime curvature increases not by its length but by the cube of its length. Thus the universe cannot consist of a more or less large scale uniform density body of infinite extent, for if it did then the spacetime curvature within it would become infinite as well, time would stop and light could not travel.

In Hypersphere Cosmology the universe has a ‘Finite and Constant’ but ‘Unbounded’ extent in both space and time.

The surface of the Earth has finite and constant but unbounded extent, you can travel as far around it as you like without encountering a boundary or an edge to fall off. Every point on the Earth’s surface also has an antipode point, the point on the other side of the world which represents the furthest away from your starting point that you can get.

Now the entire universe has a similar sort of spatial geometry but in three rather than two dimensions. You could, with a good enough spaceship and plenty of time, travel about 13 billion light years in any direction and eventually reach the furthest point away from your starting point that you could ever reach because the vast gravity of the universe causes it to curve back in on itself at that scale. If you attempted to carry on traveling you would eventually end up back where you started. However as nothing can travel faster than light this return journey would take at least 26 billion years, by which time your starting point would have few recognisable features left. Your home planet and star would probably have ceased to exist and your galaxy would have probably moved a fair distance and changed shape.

The ‘temporal geometry’ of the hyperspherical universe works in a similar way, the vast gravity of the entire universe curves time back in on itself, thus no event will appear to have occurred further away in time than about 13 billion years because the light from it will have become redshifted out of existence. However if you could somehow wait for 13 billion years you would not see the same events unfolding again, in the same way that travelling for 13 billion light years would not bring you back to anything like the ‘same’ place. Nevertheless in theory something like an ingot of tungsten drifting in deep intergalactic space could in principle persist for much longer than 13 billion years so long as a star in a passing galaxy did not suck it in, or cosmic radiation did not gradually erode it.

Hyperspheres rather than singularities will form within black holes, but no matter how much mass they absorb they will not change the overall size of the universe. Even if all matter in the universe falls into hyperspheres and the hyperspheres coalesce into each other that merely leaves the universe as a single hypersphere at the same size.

Hyperspheres with three spatial dimensions necessarily exist embedded within a spatial manifold of four dimensions, much as the curved two dimensional surface of the Earth exists only in the context of three dimensional space. We can of course dig holes some way into the planet, get some short way up into the sky or with enormous effort get a short distance into space. Unfortunately the fourth spatial dimension of a hyperspherical universe does not appear to offer any extra-dimensional travel freedom because the three dimensional space fills it up entirely, it has the same scale.

Philosophically, a universe finite and constant but unbounded in space and time leads to a rather different view of humanities place in it, to the views arising from either an infinite universe or from a universe with a beginning and an end.

A universe with a beginning and an end fits the Judaeo-Christian monotheist model and also some pagan models like the Norse one which ends with a cataclysmic Ragnarok. The final conditions implied by these philosophies suggest either historical or personal lifetime progress towards some kind of transcendence, or stoical endurance till final oblivion.

Some oriental philosophies like Buddhism and Hinduism seem to mainly take an eternalist view of the universe, cycles of creation and destruction, birth, death, and reincarnation go on endlessly with no apparently beginning or ending in sight. Such philosophies can often seem to promote a certain resignation to fate.

A hyperspherical universe, finite but unbounded in space and time, perhaps suggests other philosophical views. Finiteness has become impressed upon us by the pictures of our planet from space and the growing recognition that it cannot supply us with unlimited or infinite resources, we can go around its unbounded surface as far as we like, but we cannot go any further; we will probably have to put up with this for the lifetime of our species, for space travel will forever remain unrealistic unless fundamental physics contains some astonishing possibilities of which we currently have few inklings. Just possibly we may succeed in scaling up quantum effects to allow ‘ships’ (which will look nothing like rockets) to ‘teleport’ us across space to other star systems but this merely enlarges our non-infinite playing field.

In either case the lifetime of our species will depend directly how unboundedly we exploit our finite resources.

The questions of ‘where’ did the universe come from, or ‘when’ did it begin, now seem like the wrong questions. We have no reason to consider nothingness as somehow more fundamental than something-ness, particularly as we cannot actually observe any nothingness, and we have strong theoretical grounds for dismissing it as unnatural. Nature may abhor a vacuum but it doesn’t permit actual voids, even a vacuum contains structured spacetime. Nothingness ‘exists’ only as an abstraction, like the equally false concept of infinity.

As the universe exists as a ‘natural’ phenomenon then it doesn’t require deities to initiate it, to maintain it, or to eventually destroy it. Nevertheless they do have a more modest reality.

They didn’t make us, we make them.

Humans make gods and goddesses as tools and ‘machines’ to help them. Deities exist as Meme-Machines that have many societal, cultural, and personal functions. They can coerce or inspire not just individuals but entire societies to do or to not do a vast range of things.

Memes, like Genes, evolve by a process of mutation and selection, and basically we apply both the mutations and the selection pressure. Deities that have become ineffectual or whose characteristics have become a survival liability tend to die off, whilst new ones become created from the mutated wreckage of the old, although the devotees of a new or improved deity usually prefer not to acknowledge this.

Our imaginary friends have enormous real effects, so we need to design them carefully.

Newton’s god, so far as we can tell, seems to have had the characteristics of some kind of rational ‘Architect of the Universe’; Newton certainly rejected the messy doctrines of the trinity and the divinity of Christ.

Newton’s vision pretty much encapsulates The Enlightenment’s religious position.

Einstein did not believe in a personal god, but rather he adopted a Pantheistic view of an ordered cosmos, divine in itself. He could never quite accept that the universe behaved with a degree of randomness as the quantum physics which he also initiated, seemed to so strongly imply.

Einstein’s vision pretty well encapsulates the New-Age Humanist’s religious position.

Hypersphere Cosmology, well it suggests that the universe does not require a designer and that its quantum behaviour suggests that it does act with a fair degree of randomness, but in a way that makes it more rather than less divine in itself. A totally causal deterministic universe would have only us, or perhaps not even us, to make it unpredictable. Plus we can make gods and goddesses to our hearts delight and terror.

Chaoism? A work in progress…….

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