Monday, March 5, 2012

Visualizing the Fourth Dimension

I was thinking about Picasso today. As his artwork was explained to me, he was attempting to show three dimensional objects in a two dimensional painting from multiple perspectives. This is why they seem to be distorted and do not make normal visual sense to us.

As I was thinking about Picasso, I realized that he may have been attempting to illustrate the appearance of a three dimensional subject from the perspective of a fourth dimensional being. If we assume that when I say fourth dimension I am not talking about time but about a fourth physical dimension, then that dimension must exist at a perfect right angle from the three dimensions we know.

If you have not yet watched it, I would reccommend Carl Sagan's brief description of Flatland, which was aired in an epsiode of Cosmos. Flatland is a story that was written in 1884 by Edwin Abbott. (Flatland) The story describes beings who exist in only two dimensions, length and width. They are aware only of X and Y axis with no concept of the up/down Z axis. With an understanding of how a three dimensional being would appear to them, we can then formulate how in our three dimensional world a fourth dimensional being would appear to us - partial, incomplete, and very strange.

We can also imagine how we would appear to a fourth dimensional being - entirely complete as a whole from all three dimensions when we can only see ourselves as two dimensional at any given time. It is a trick of our two eyes that allows us to perceive three dimensions, yet we can only actually see two dimensions at once.

Everything to us is like a screen on a television, a moving picture, that just so happens to wrap slightly around our curved line of vision. Because our eyes are set apart and see two different images of this three dimensional space, they are able to show us ever so slightly two angles of our world. This is what allows us to have depth perception: if something is near to us, we see the difference in those angles more distinctly. If it is farther away, both of our eyes see essentially the same thing. To our minds, a distant object appears flatter than a near object.

In art we illustrate three dimensions using only two. Thanks to perspective and shading we can give our minds that same perception of depth that is created by the placement of our eyes. The more accurate the perspective and shading is in a painting the more realistic it looks to us. This is why some two dimensional images (photographs) register as being very real whereas some two dimensional images do not. CGI is capable of fooling the eye with perspective because we can design computer software that "comprehends" three dimensions: effectively we can create a three dimensional world inside of a computer through the illusion of the programming. We can only view it from a two dimensional perspective of our computer monitors and televisions, but because the program is designed to show a three dimensional space it looks three dimensional to us.

This got me to thinking: If we can program software to understand three dimensions, can we program software that extrapolates into four dimensions? If not today, I believe this will be possible someday. In computer software, we're working with virtual space rather than true three dimensional space. At the moment we are incapable of describing what the direction of this fourth dimension is, but we can grasp that it exists. The example for this is the tesseract. If you watch the aforementioned video of Carl Sagan's explanation of Flatland, at the end he speaks about the tesseract or fourth dimensional hypercube. In the same way that we can cast a two dimensional shadow of a cube, the three dimensional tesseract is a shadow of the fourth dimensional object. Interestingly, illustrations of the fourth dimension tesseract show it to be continuously in motion in order to attemtp to fully describe its form. THe object appears to oscillate, constantly turning itself inside out. I think that our ability to understand the fourth dimension will require some type of oscillation through the viewpoints as our eyes are incapable of viewing a four-dimensional object from what is essentially a two dimensional perspective.

The fourth dimension as time

It is generally accepted that time is a fourth dimension to our three dimensional world. If we consider this possibility, then it makes certain ancient concepts seem to have been describing the view of something from these four dimensions. There are the trinities: Maiden, Mother, Crone; Son, Father, Holy Spirit; Brahma, Vishnu, Shiva. Each of these trinities describes three points in time of a singular being, in a visual sense.

The easiest to describe is the Mother, Maiden, Crone. You have the Mother - the middle aged or mid-life female, her earlier form in the Maiden and her later form in the Crone. With Brahma, Vishnu and Shiva, you have Creator, Preserver, Destroyer. In the Son, Father and Holy Spirit you have the youth, the older middle age, and that which exists beyond death.

Each of these deity descriptions describe a singular being in three points of time yet existing simultaneously - which from our perspective is impossible. Or is it?

In our own minds we have the memories of our past time-forms and the expectations of our future time-forms. Within our own minds, past present and future are all conceivable even if they are not completely knowable. In philosophy this is called endurantism; all temporal parts present within the entirety of our existance.

Hopefully one day we'll have a better idea of other dimensions of our universe or possibly even other universes. For now, we can read about the discoveries and theories as they develop and in our own minds try to imagine what reality would be like from a fourth dimension.

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