and put the football inside it. If you can now imagine the football simoultaneously occupying all the possible positions within the larger sphere, you have just seen a glimpse of the fourth dimension! Sadly it is impossible for us to see the simoultaneous occupation of plural spaces by one object due to our limited perceptive powers. Only if we were made of light could this be possible. But by freezing this movement we can look at a slice through a four dimensional sphere. In a similar way, if there existed “flatlanders” (and I very much doubt it) these creatures would live on a flat 2 dimensional reality. My hand is a unit, but if I placed the fingertips of my hand on their world, they would sense five individual circles that were obviously separated from each other. Only later if I continue to introduce my hand would my fingers eventually join up to form something completely different and “unitary”. They could never see my hand simoultaneously. I know that this subject is infuriating difficult to imagine; the good news is that I’ve nearly finished with these extrapolations.
As there is an enormous amount of literature about angels, guardian angels, spirits, ghosts etc in every language, culture, and religion and epoch in human history, I do not wish to dwell on their nature too long. I only wish to suggest that if they do indeed exist it is to aid us poor, blind humans in our decision-making. Maybe they are the passengers in the analogy of the horse and carriage. This would go some way to explaining things like inspiration and various ESP phenomena, but also how from the total chaos of human interactions, miraculous discoveries are made often associated with strange co-incidences. Maybe the highest vibrations of human consciousness correspond to the lowest vibrations of angelic consciousness. This is maybe why only after a lot of hard work do “flashes” of inspiration come. Often after the big moment of “eureka”, we wonder why we hadn’t thought of it sooner! To me, this is typical of our ability to do things with a sense of arrogant self-criticism. Here is one of countless moments of breakthrough, in the field of mathematics.
Henri Poincaré, the great French mathematician, described the moment of sudden illumination that came to him as he stepped on to a tram: “At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts, seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry.
“I did not verify the idea…I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for conscience’ sake, I verified the result at my leisure” Quoted in Hadamard “The psychology of invention in the mathematical field”, 1945
Another more famous discovery by Freidrich Kekulé came whilst on a bus, (is this just a co-incidence?) but in this case Kekulé was half asleep and “dreaming” of snakes biting their tails. This he saw as being an explanation of the form of the aromatic compound benzene and its ring structure, which until then had remained a mystery.
Finally, a young Steven Hawking whilst sat on a train had a sudden insight when a passenger sat opposite made a remark about traveling backwards. Allegedly, this helped him conceive the idea that the “Big bang” was theoretically plausible.
Why public transport seems to inspire people is still a mystery to me.
ARC-ANGELS =6TH DIMENSION
If a 5 dimensional surface represents one multi-verse, i.e., an infinite number of universes running in parallel with each other, then a 6 dimensional “solid” represents an infinite number of multi-verses. One multi-verse contains all the possible choices available in it, but it does not contain an infinite variety of physical laws governing it! i.e., the very nature of the matter composing each multi-verse. Describing a conscious 5 dimensional being living “trapped” in the 6th dimension is way beyond even my vivid imagination’s scope to give you a taste of its day-to-day lifestyle. However, these beings would not only be able to perceive an infinite number of universes as simple objects, but would perceive an infinite variation in their very fabric, as “time” goes by. Maybe their role is to act as quality control technicians, whose responsibilities are to keep an eye out for multi-verses whose physical laws are “life friendly”!
Cosmologists have long been perplexed by the fact that the laws of nature seem to be cunningly concocted to enable life to emerge. Take the element carbon, the vital element that is the basis of all life (as we know it). It wasn’t made in the Big Bang; instead, carbon has been cooked inside stars, which