A Flatland Motivated View Of Determinism

One of the greatest questions in philosophy is that of determinism. Is everything in our world pre-determined? Is our universe simply a collection of giant gears and levers which continue to turn and entirely determine the future? This may be an impossible question to consider, as I will illustrate using Flatland.
For the benefit of the reader who is unfamiliar with flatland, I digress momentarily. Flatland -- A Romance In Many Dimensions is set in a two dimensional world, which is inhabited by simple polygons. These polygons possess a given number of sides based on their importance in society. For example, women exist as a line segment and are the lowest beings in society, whereas priests -- always male -- are circles -- an infinite sided polygon. The main "character" (a humble square) has a series of dreams and visions, in which worlds of 0, 1 and 3 dimensions are revealed to him. After observing "spaceland" the mundane two dimensional world is no longer enough for him. He wants more!
I, the author, too want more. What is the fourth spacial dimension really like. One can construct simple analogies by extending two dimensions to the third, however this does very little to give one a fourth dimension impression.
I now return to the main focus of this article -- determinism as inspired by Flatland. Consider this two dimensional Flatland, and its inhabitants. Pretend they have been squabbling for years, and are divided by this fundamental philosophical question. One side believe that everything is determined, whereas the other side argue "NO! I know I have free will. Furthermore, I know for a fact that the universe is not deterministic -- I saw a priest appear in my house just the other day. He just appeared there... materialised out of nothing! Whats more, he grew bigger and bigger, until suddenly he started to shrink again, and finally disappeared" Indeed, for a body to suddenly appear in your lounge room at random does seem to be rather conclusive evidence against scientific determinism. We here in Spaceland, however, observed the very incident to which the Flatlanders are referring. We know in fact that the "priest" which the Flatlanders observed was not a priest at all. It was a sphere (bearing in mind that Flatland priests are circles) passing through the surface of Flatland! Obviously, to the Spacelanders, it was entirely predictable that the spheres projection on Flatland would be a circle. It was predictable that as the sphere passed through the surface of Flatland the circle would expand until Flatland passed the spheres diameter, at which point the circle would shrink again. It was even predictable that Flatland's inhabitant would argue over the origins of the "priest" as if it was a random appearance of a divine being.
For now I will leave you with the following thought, and save for next time the implications that this has on free will. Can we sensibly argue against determinism? Even if we concluded that, in our observable dimensions, things were definitely not deterministic how can we refute the possibility of determinism in a higher dimensional space?

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