The Spaces between Space

The notion of alien geometries is something comes up in science fiction stories to reference places that don't exist in the universe as we know it.  A simple example is the artwork of M.C. Escher which in turn has been translated into a PSN puzzle game by the name of Echochrome.  By shifting the view point around players are able to impose forced perspective tricks on the environment.  It's a clever idea, but for the purposes of this blog entry I want to explore the concept in video games a bit further...into higher dimensions.  Be forewarned a lot of science talk is coming up so put on your thinking caps.

Before we jump into the deep end though let's think about perspectives.  Humans have awareness and mobility in three dimensions, meaning we can see and move up and down, left and right, as well as forward and back.  We perceive time, the fourth dimension, in slices.  How big a slice depends largely on the activity of your brain.  Under extreme duress the slices might become very thin, stretching seconds out into what feels like minutes.  Meanwhile, sleeping thickens things to the point where hours pass in the blink of an eye.

To help explain what's coming next let's do a quick though exercise involving tiny hypothetical 2D creatures.  Imagine these flat little guys live on a sheet of paper.  Because of their nature they can only see and move forward and back, as well as left and right.  Everything above and below them doesn't exist from their perspective.  Now imagine for a moment you were to press your finger onto the paper in front of one of the creatures.  From its perspective it would appear as if a large amorphous blob had suddenly materialized in its plane of existence.  Then, of course, lifting your finger off the paper would promptly cause the blob to disappear.  I imagine that the creature would find this rather unsettling and if possible would want to communicate this disturbing event to its fellows.  The witnessing creature's faculties might be called into question, but assuming that such occurrences are a rarity in this 2D world; ghosts, UFOs or even magical interpretations aren't out of the question.  This might sound slightly mischievous or cruel, but a much more devious thing to do would be to bend and twist the paper 2D world on which these creature live.  Again, to them nothing has changed, but if you are operating in 3D (or higher) then things are definitely different than they were before.

In Siren: Blood Curse this kind of effect is represented by a kaleidoscope when the human protagonist of the story is pulled into the lair of the last boss, an alien being that inhabits a higher number of dimensions than four.  Dazzling color displays aside, this final opponent has the ability to seemingly break itself into pieces and then reassemble into several radically different combinations.  In fact the pieces aren't actually breaking apart, rather the player simply cannot see the connecting tissue because it does not intersect with the human plane of existence.

The term non-Euclidean is sometimes used to describe this hypothetical phenomenon since it literally means two lines or, by extension, planes that do not intersect.  The horror novelist H.P. Lovecraft used this kind of terminology to describe the sunken city of R'lyeh.  According to the text the buildings consist of various monolithic stone structures that have angles and gaps that would ordinarily cause a structural collapse.  However, this isn't the case because the buildings are supported in ways our mind can't process visually.  Indeed, in the story stepping through these weird cracks in the architecture can cause a person to come out in an entirely different location.  Obviously this makes it very easy to get lost.  In the point-and-click game The Dig, aliens attempting to explore six dimensional space find themselves lost and unable find their way back to normal space without the help of the player.

Obviously, all this is a bit difficult to imagine in your head, but there are several video game rendering engines that can produce weird geometric effects like Klein Bottles or "spiral" hallways that require 720 degrees of rotation to complete a full circle.  Don't believe me?  Check it out for yourself:

Are you thoroughly disoriented yet?  No!?!  Well, here's one more for you using the Portal 2 engine:

Now, if your sanity is still intact I think it's safe to say that you're a fairly logical minded person.  Whatever you think though don't dismiss all this as a bunch of improvable nonsense.  After all, only about 10% of the matter in the universe is accounted for.  While a number of astronomers have speculated on the nature of black holes and the average number of planets in a given solar system, I think using the catch-all term Dark Matter is a bit misleading because as the game footage above demonstrates, it might not be about light emissions but rather spacial locations.