Anyone who comes from my native town, when asked what their homeland looks like, are likely to answer: “It’s a Flatland.”
Honestly, I couldn’t find a better word to describe it: Flat.
Even the buildings barely dare to rise further than the third floor, as if they believed it wasn’t possible to get too far from the Flat ground.
Now, this is clearly an exaggeration. Of course it is. Even though my hometown is actually quite plain, it still retains its third dimension.
What would it be if it didn’t? How would it look like a world actually Flat, in solely two dimensions?
Edwin A. Abbot answered this question. And the answer is: foggy and linear. And quite dumm, too.
In his mental exercise ‘Flatland’, Abbot is a Square, his wife is a straight Line and his grandsons are Hexagones. The houses are pentagons and the priests are Circles.
The concept is simple: if you are born Square, you’re going to be a Square for the rest of your life, bounded to the condition and the status given to a Square. With some luck, your sons will aspire to the status of Pentagons.
If you are born a straight Line, then you’re a woman. And of course you’re going to be a straight line (and a woman) for the rest of your life. But it’s ok, because due to geometrical reasons, you won’t have enough brain to get upset about it.
In Flatland you can only move left and right, Northward and Southward. As floating on the surface of a table, never detaching from it.
If you ask about the meaning of Upwards, they’ll say you’re mistakening – you must be meaning Northward.
And if you ask any of them what’s the meaning of a third dimension, they’ll either laugh at you, or report you to the authorities for blasphemy.
“There’s no such thing as a third dimension” says the Circle in Flatland.
Yet, “there’s no such thing as a second dimension” says the King of Lineland, happy enough running back and forth on his straight line, where only one dimension is allowed.
Flatland is not just a two dimensions world, where it’is particularly difficult to do the difference between one another – it looks like a straight line, from wherever you take it.
It is a state of mind. Fixed. Unchanged. Unmovable.
Until one day it happens that someone succeeds to go Upwards, instead of Northward; to go Left instead of Forth. To transcend the imposed limits and get to the next dimension.
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