You may or may not have heard the allegory of the Cave wall from Plato’s Republic, but I will sum it up as follows. You are a prisoner, you have done nothing wrong, but instead were born in the prison which holds you, and have been here all your life. In this prison you are chained to a low stone wall. so that the only light you can see is the light that the cave wall catches. The source of the light comes from behind the wall to which you are chained. every day you interact with the guards from this position and see them pass by only as shadows on your cave wall. Now, given this situation, if all you had ever known was these shadows who seemed to posses voices you would believe, mistakenly that this was all there was to the world. You might think that the world was two dimensional and that you were some sort of horrific creature who is imprisoned for possessing a third dimension.
This Plato argues is what the physical world is like. He believed the the true world, the world of the guards on the other side of the wall, was a one of pure ideals and geometries. He believed that our wall was just like the prisoners shadows, merely a projection of was is truly there and that the only way to see the true world was through logic and reason. Plato thought that if we could see this true world as we see the physical world, that it would be like the prisoner being brought out to look at the sun, and that we would go blind from its brilliance. He thought that as a philosopher he was one of the few with the power to see this world, and bring back its knowledge to the benefit of mankind.It is a beautiful analogy with and equally beautiful Logic behind it. It reminds me of another story from a book called Flatland: A Romance of Many Dimensions, which follows the life of a square. The book describes the society of this two dimensional world, and once you get passed the fairly racist and very sexist world views that the author clearly possessed, you are familiarized with this two-dimensional world so that you begin to think two dimensional. And if the book stopped here it would be a quirky fiction about a two dimensional world populated by regular geometric figures.
Spoilers below, the book is fairly short and if you want to give it a read first, it is available in full from google.
But the story continues and the square with which we are concerned has a vision of a one dimensional world which exists as an infinite line populated by line segments he interacts with the king of Lineland and despite his best efforts he cannot get the King to conceive of a second dimension and concludes that the square, who simply appears to be a line segment himself that can disappear at will by passing into and out of the infinite line, is mad and dismisses him from his presence. As the square is leave this world of lines he happens across another world, Pointland. the world exists as a single dot and is populated by as single entity, the squares conversation with this second creature is even more brief and frustrating, as he cannot even get the point to concede that the square is not just another voice in his own mind let alone that there are such things as dimensions. So having had these disturbing visions of other dimensions he struggles with their meaning and with whether or not these worlds exist or if it was all just a dream.
Then not long after his journey into the lower dimensions the square is visited by what he first perceives to be a line (the females of his world) when he realizes that what he is really seeing is a Circle (who are considered to be royalty since status is determined by the number of sides one possess, and anyone with more than 100 sides is a circle). After dealing with the shock of a circle suddenly appearing in his home he begins to converse with the gentleman and discovers that he, the circle that is, has the ability to change his size. The circle begins to explain that he is not a circle but a sphere and possessing three dimensions. The square, just as the line and the dot, can not conceive of this third dimension he calls depth and becomes quite frustrated with the conversation.
To show him the truth of the matter he brings the square out the plane which is his universe, giving him three dimensions and allowing the, now, cube to see this world in which the sphere lives. The square after being returned is eternally grateful to the sphere and praises his deed, but then asked if the sphere can show him the higher dimensions, the fourth and fifth, he begs. But the sphere can not understand what the square is talking about, he can not conceive of a higher dimension himself, and without the help of some fourth dimensional being, he will never be convinced.
The analogy here is obvious without having and reference point to relate it to trying to peer beyond our own three-dimensional physical world is only ever “possible” in theory. Using logic and reason, as Plato might have phrased it, is the only means we have of seeing beyond.
And that’s my take on Plato’s Wall