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The symbol shown here represents a Hypersphere, sometimes called a three-sphere, or a 4-ball, or an S3 manifold.In such a hypersphere the internal 'diameter' or Antipode length equals half the circumference, making it somewhat 'larger on the inside than on the outside'. Its resemblance to the Taoist yin-yang symbol seems most pleasing, the classical oriental mystics thought of most things at one time or another although not always in simple to understand terms.
The Hypersphere Cosmology section of this site now contains several new papers dealing with aspects of the main hypothesis in more mathematical detail and with more detail on the physical principles implied.
Hypershpere Redshift shows the mechanism by which the small positive curvature of the non-expanding universe redshifts light from distant galaxies.
Hypersphere Rotation shows the derivation of the equation for the four-rotation of any hypersphere derived from Godels three-rotation of a simple sphere. Any valid derivation from an exact solution of the field equations of General Relativity presumably has its own exact solution in there somewhere.
Hypersphere Holometry derives from the Beckenstein-Hawking conjecture about the relationship between the information content of a black hole and its surface area. If true, and if applicable to hyperspheres, the conjecture leads to a prediction about the quantisation of space and time which Holometry experiments in progress may validate.
Hypersphere Visualisation and Lensing shows a fairly simple method of visualising what a hypersphere 'looks' like, and the lensing diagrams show how a hypersphere will distort sight lines across the universe creating the optical illusion of an apparent acellerating expansion.
On an entirely different matter Pactionis 2, first presented on a blog here in 2013, reappears in the Wizardry section, because it needs to.
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Hypersphere Cosmology
An exhausting 30 day battle has just finished on the Cosmo Quest Physics Forum:
(See ‘Against the Mainstream’ section.)
This battle, fought mainly with n-dimensional algebra through many a sleepless night, ended with the massed advocates of standard cosmology at a standstill and throwing in the towel by invoking a 30 day rule to avoid a retreat.
During the conflict, worldwide mass googling of ‘hypersphere cosmology’ brought the following obscure scientific paper, published in June 2014, out of the woodwork and up the rankings:
www.scirp.org/journal/PaperDownload.aspx?paperID=48375
‘On the Physics inside a Closed, Static, Rotating Einsteinian Hypersphere in Due Consideration of the Galaxy.’
Beneath the blizzard of algebra and differing notations in this paper, it seems obvious that its theory exhibits almost complete isomorphism with hypersphere cosmology as presented on this site, and previously published in outline form in a natural philosophy treatise - The Octavo 2011.
It would seem that the Natural Philosophy approach and the Hard Science approach have come to identical conclusions here.
Natural Philosophy theory tends to start with physical principles derived from reason and imagination and then tries to wrap some maths around them to check their validity. Hard Science theory tends to start from accepted physical principles and then tries to extend them by mathematics.
Because we can think of far more physical principles and far more mathematics than the universe actually uses, both endeavours can run into problems. Both approaches require the reality checks of plausibility and experiment.
The hypersphere cosmology hypothesis began with the natural philosophical intuition that the physical principles implied by the initial conditions of the big bang theory remain totally implausible.
We can only rely on ‘The Unreasonable Effectiveness of Mathematics’ when they don’t lead to implausible solutions that require dozens of equally implausible patches to shore them up, like singularity theory, cosmic inflation, dark energy, and dark matter.
We may now confidently expect the replacement of all variants of the big-bang-expanding universe theory with variants of hypersphere cosmology theory within a few years.
This may upset a number of older physicists but it will provide plenty of work and excitement for the coming generation of bright young physicists.
It may also upset the Pope a bit, which seems a pity because the current one seems a nice humanist type, but nobody has infallibility, and maybe the idea of a deity who doesn’t start the universe with a cataclysmic explosion and who doesn’t end it all with a feeble entropic fade out or a crushing collapse, may catch on.
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Herewith Lugh, one of a series of Celtic Gods associated with my area as the pan-celtic god Lugus and his welsh counterpart Lleu.
In the recorded Irish myths he appears as the thinking man's superhero - a wright, a smith, a champion, swordsman, a harpist, a hero, a poet and historian, a craftsman and a sorcerer.
Anything you can do Lugh can do better - as the Prof has quipped.
In this faux first century bronze (rendered in metal and milliput) I've depicted him with a mercurial style magic spear (the Romans equated him with their Mercury) and a slingshot at his belt and a harp for his atributes in the Irish myths.
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As no tenured academic seems to want to risk career suicide by endorsing the following scientific paper for journal publication I release it here into the public domain for free use.
http://www.specularium.org/hypersphere-cosmology
It's located on the Hypersphere Cosmology section of this site.
Unfortunately its radical conclusions may invalidate the current work of some 20,000 or so theorists, however it will give them plenty to do with the rest of their time.
Perhaps doubly unfortunately this all comes from an old style Natural Philosopher and Wizard, but don't let that inhibit your rigorous investigation of the maths and physical principles that it implies.
And on a lighter note see my impression of Sulis, Goddess of the hot springs at Bath, 1st century romano-celtic bronze in the neo-barbaric style :) actually rendered in milliput and steel wire framed, black lacquered and verdigrissed, I hope they like it at Grove. Impression of Lugh to follow.