In this closing part of my trilogy about the concept of a dimension I want to explore the psychological, religious and cosmological implications of the word. That will draw a lot upon the prospects and explanations in part one and two. So please read them first.
In the beginning of the western philosophical tradition things were well ordered and even static, because the term was only used in the context of planar constructions and solids, one could measure without haste. dimensio applied just to the tangible domain. In opposition to that, enumerable relations between music notes were called modulatio, as 4th century church father Augustine echoed the already thousand year old Pythagorean teaching.
Through the tangible world we navigate via deep instincts, that underly our conscious decisions. This is one reason why the word dimension is so powerful. Mathematicians use that, to attach meaning and memorability to their concepts - even and especially when they move away from the tangible. This I already layed out in the final pragraphs of part one.
Our forefathers in antiquity did pretty much the same, but for spiritual purposes. Their task was to provide the laymen with a language for their inner experiences, that could be shared with priests. To integrate into common experience, they couldn't go outside 3D. So they used the vertical dimension to descibe 'movements of the soul', which leaves the horizontal 2D for the physical world.
Please note this is very different from the views of todays flat earth society. When Eratosthenes of Cyrene calculated the circumference of the earth, he faced no trouble with organized religion, because it was widely understood that a world as a plane was a metaphor. That got l bit lost in later cultures, when the map of Claudius Ptolemy was taken as physical truth. I think he described the movement upward along the spiritual dimension, because other depictions describe the same planetary spheres above the earth and continue with the 'fixed stars', then with the traditional angels hierarchies, leading up to a huge sitting Jesus Christ. A long ladder (which refers to the book of Ezekiel) between Earth and Christs lap with climbing and descending beings is suggesting, that this was meant as a map of experiences (or at least spiritual places). This basic notion was shared by most ancient cultures. The Celts for instance saw Asgard (place of gods) above Midgard (this world) and a big (vertical) tree Yggdrasill did connect these two with the other seven worlds.
With such a cosmology it is not unreasonable to imagine our world as flat. It looks flat - even from a mountain. And more importantly, whenever we move fast and easily, we move only vertically. Every horizontal motion of our body is attached to a special effort. This is engrained in our motorcortex and language. If someone talks about deep thoughts or high consciousness it's instinctively understood, that the speaker refers to something that is potentially reachable to everyone who is able and willing to put in an extraordinary amount of effort.
And that might be one reason, why the hero Heracles (after proving himself worthy of the title) was elevated by the gods and became a star constellation we still recognize. He overcame his epic adventures not only by strength beyond human nature, but also with foresight and a cunning intelligence. His heighten position on the night sky could not only be the testament of his exceptional efforts but also his mental state. If we concentrate - we can reflect upon the past, plan our future and overlook great landscapes in our imagination. But more likely it refers to some lofty state, where you feel no worry and issues of daily life feel easy to nonexistent. That would be just logical, since the level of the 'fixed stars' (canopy) is classified way above the sphere of mercury, that is normally associated with intellectual activity.
Without getting too speculative, we have a sence where sexuality is taking place, that greed is felt in the guts, that love is emitted from the heart, if we touch our head, its widely understood that we refer to our thinking. Due to our upright posture, inner processes can be mapped along the vertical dimension, in a way that can be understood instinctively. From this standpoint it is logical, to locate a heavenly and hellish states along this axis, just outside the ordinary reach.
That heaven is placed in the direction the head is 'heading' and hell in the direction our bottom is pointing at can be intuited in the same way, as illustrated by the story of a japanese worrier asking a monk to show him heaven and hell. The monk immediately starts mocking the worthiness of the questioner, which in return reaches for his sword to behead the brazen one. Seeing that, the monk firmly says 'this is hell'. The warrior understands and smiles, whereas the monk replies 'and this heaven'.
After establishing that spiritual processes were mapped upon the vertical axis, and that worldly motions are practically horicontal, we get a sense why Jesus is depicted on a cross. He, of whom is said he helps us to reach a diety otherwise unaccessible, sits at the crossroads of this world and the heavens beyond. And when saying give Caesar what is Caesars and God what belongs to God he seems to promote a truce between worldly and spiritual aspirations.
As a last remark I want to refer to some Bible commentary, that talks about six dimensions. While enumerating the directly understandable directions of North and South, West and East, above and below it tells us also about the dimension of start and end and good and evil. While 'start and end' can plausibly be decoded as time - 'good and evil' is a bit harder to crack. Since good people go to heaven and the bad ones not, this could be the spiritual dimension this whole text is describing. Interestingly, here it is no longer mapped on the vertical axis. This might have something to do with the circumstance, that rabbinic literature is not meant for widespread consumtion.
I found the question intriguing: what was meant by good and evil. It had to be something referenceable with motion like space or time. To answer that, we have to look, (of course) into the Bible, book 1: Genesis. In the first chapters God labels every creation as good, well except the fact that man was alone. And shortly after eve was created the snake came along and evil entered the human experience when adam bit in that apple. Whatever is meant by apple, it moved fom the outside into adam, along the fractal dimension if you will (see last paragraph part two). And if you think about, it seems like an accurate description, even by todays standards. From all the hard to describe directions your mind can take, you can distinguish spacial dimensions, time and movements from the concrete to abstract.