The Shape of the Universe
In this section all our Flatland-derived principles are brought to bear on the observer’s experience of the universe. Since a cross-section of a hypersphere is a sphere, the question is asked, ‘What if the observable universe is a cross-section of the universe proper?’ This leads to an observer-centric model which corresponds to Einstein’s description of a universe based on sphericality. (Although this was the model he favoured, a lack of data meant he left it to the astronomers to decide between this and the infinite model; they chose the latter.)
Extrapolating up from the globe, the model that emerges – which I refer to as the ‘twin demisphere model’ – divides similarly into two hemispheres, consisting of the two spherical ‘hemispheres’ of a hypersphere. These spheres – which are geometrically up by one dimension from the northern and southern hemispheres of a globe – have their poles at their centres but crucially share the same surface: their 2-Dimensional equator.
Naming these centres Centre A (the origin, or north pole) and Centre B (the observer, or south pole), I then show by the experimental process of ‘rolling the balls’ how the northern demisphere would appear from the centre of the southern. Viewed in every direction from Centre B, the north pole origin at Centre A thereby appears to the observer projected over the whole sky, lensed by the ‘Antarctica effect’. As the light all left from the same source to cross the 2D equator before converging on Centre B, this phenomenon explains the uniformity of the cosmic microwave-background radiation (CMB), supplying a simple, non-arbitrary, Flatland-based alternative to the theory of Cosmic Inflation. Also, as the model is finite, it dispenses with infinity and the multiverse.
The section concludes with a comparison of the twin demisphere model with Albert Einstein’s 1916 description of a spherical universe, finding them to be the same.
The State of Play