Plato, the Father of the Fourth Dimension

Plato. Luni marble, copy of the portrait made by Silanion ca. 370 BC for the Academia in Athens.

Plato was the father of both Alternate Dimensions and the Fourth Dimension. The otherworldly nature of these two binds them together like the single side of a Moebius Strip.

Readers of my book, The Gnostic Notebook: On Plato, the Fourth Dimension, and the Lost Philosophy, will recall the various connections between the works of Plato and the 'discovery' of the Fourth Dimension. These connections include the Analogy of the Cave with its depiction of prisoners entranced by the shadows cast on their cave wall. The prisoners mistake the shadows for the real three-dimensional world. In just this simple description we have two key techniques for the analyzing of higher dimensions: Projection, which is related to the casting of shadows, and Dimensional Analogy which is where we imagine how a two-dimensional being would experience a three-dimensional object as in Edwin Abbott Abbott's Flatland.

It was also Plato who, with the formation of his academy at Athens, set into motion the collection and development of mathematical and geometrical knowledge which resulted in Euclid's Elements. This led, after a couple of thousand years, to the creation of the Cartesian coordinate system. 

Plato was also the first to come up with the idea of an alternate dimension. He called his the World of Forms and identified it as a dimension filled with eternal and unchanging archetypes such as Truth, the perfect circle, the number 2, and the Pythagorean theorem. 

The point of having the World of Forms is to be able to able to have a realm of absolutes outside of the material realm. That way one can recognize what is good because one has knowledge of the Good from the World of Forms and then one can find that which resembles the Good in the material realm.

This was all in an attempt to get to the essence of a thing. When we speak about something, we are using words to describe the thing. These words are themselves descriptions of aspects of the things, but how do we know that these other words correctly capture the essence of the aspects they describe? The deeper we go into examining the terms, the more obvious it becomes that these terms are just words used by those who came before us, none of which can bring us any closer to the thing's essence. Hence the need to jump out of the Universe to the realm of absolutes where the unchanging truth dwells. 

Before Plato, the entire concept of a separate alternate dimension didn't exist. God was on top of a mountain, Hades was beneath the earth. 

After Plato came the Christian heaven and hell, realms of eternal bliss or eternal suffering. Eternal because they exist outside of the material realm and therefore outside of time and space.

It seems as though these three aspects of Plato's philosophy: the dimensional aspects of the Analogy of the Cave, the alternate dimension of the World of Forms, and his support of research in mathematics and geometry which culminated in Euclid's Elements, apparently led to both the 'discovery' of the Fourth Dimension and the proliferation of alternate dimensions. 

Moreover, the concepts of the Fourth Dimension and Parallel Dimensions are closely intertwined. We live in a space of three dimensions. Up - Down, Left - Right, and Forward - Back. Just like the citizen of Flatland who cannot perceive the Up - Down dimension, it may be that there is a hidden fourth perpendicular along which we can move. If so, that may mean that these parallel dimensions are quite close to our own when we move along this fourth dimension, though they remain unreachable from the usual three.

Using this sort of reasoning, it soon becomes obvious that Heaven and Hell must exist within the Fourth Dimension. As to the existence of the Fourth Dimension itself, we will consider that impossibility in the next post.