Riemann, Bernhard - On Riemann geometry
Type of Spiritual Experience
The approach of theoretical physicists, has been to set about producing theories which attempt to explain all the anomalies and observations they could not account for by extra physical dimensions in space time – so not dimensions to be found in the spiritual world [which was rejected as superstitious nonsense] but actual physically existent dimensions which were invisible because they were, for example, ‘behind’ wormholes and black holes.
In some cases, they based their theories on formula that the mathematicians had provided.
It is clear from studying the mathematical proofs produced prior to this period, however, that the mathematicians themselves presupposed no such extra physical dimensions, they simply attempted to mathematically provide certain rules by allowing for more virtual dimensions. Mathematical geniuses such as Bernard Riemann produced enormously important geometrical proofs which paved the way for Einstein’s theory of relativity.
Unfortunately, many theoretical physicists have taken the mathematical need for extra dimensions totally literally and assumed that the extra dimensions physically existed.
No computer programmer would ever have made this assumption and quite a number of software systems use n-dimensions. I have used n-dimensional spaces, for example, in order to be able to record the existence of versions and configurations of the systems themselves. You can never physically represent these dimensions because they are virtual. You can create any number of dimensions using software.
In essence the big difference between mathematicians, computer scientists, many of the better philosophers, all mystics and all the religious community on the one hand and that of the theoretical physicist on the other hand is that the physicists rely on a ‘physical’ world and deny the existence of anything that might be termed ‘virtual’- so ‘thought’ as opposed to matter.
A description of the experience
Internet description - 'the genius of Riemann'
No one single experience occurred to Riemann, but despite or perhaps more correctly because of his physical handicaps, Riemann showed from a very early age that he was a genius at mathematics.
He was able to solve complicated mathematical calculations, often surpassing his instructor's knowledge. The turning point came when one of his instructors gave him Adrien-Marie Legendre’s Theory of Numbers. He read it in 6 days.
He found the correct way to extend into n dimensions, the differential geometry of surfaces and his work set the stage for Einstein's general relativity. Einstein used Riemann geometry to explain the nature of ‘four dimensional’ space.