Introduction
Hyperspace is space with more than three spatial dimensions, as some of you who have taken the final hours of calculus and/or linear algebra are familiar with. As far as we know, it only exists within software, and if you are disciplined enough then also your mind. In three dimensions, six perceivable directions exist: up, down, left, right, forward, and backward Add to that kata and ana for the fourth dimension. There are different existing mathematical structures for 4D space. Overall, Euclidean space is commonly used, especially in interactive software. I personally have made sense of the different types by grouping them into what I call "on the surface" and "beneath the surface."
On the surface refers to an existing fourth dimension that you don't actually see. It allows you to traverse between parallel 3D worlds, where you only see 3D space, 3D objects, and 3D physics. It would be like popping in and out of 3D worlds by moving or rotating through the fourth dimension. This can either happen through "sideways" time, seeing alternate versions of the same world through different past events, or through seeing a different pocket 3D world entirely, similar to perceiving teleportation, although that is not actually what happens.
Beneath the surface refers to a full-on 4D experience, seeing in 4D space with 4D objects and 4D physics. This is near impossible to display entirely without some form of transparency and color shifts to positive and negative direction in the fourth dimension. This is taught in the final hours of calculus with graphing, which, to my surprise, many who are familiar with 4D space have taken yet do not use this feature in many of these programs. Most of the softwares below are some combination of both on and beneath the surface. To future game developers: showing the fourth dimension in a 3D setting with transparent overlays and color shifts would be optimal in an RPG setting.
Why is understanding hyperspace important?
Understanding hyperspace broadens our capacity for thinking and is a necessary component in our conscious evolution. Learning and practicing mathematics has always concerned increasing our capacity for problem solving, and understanding 4D+ space is no different. With it, we can imagine and create new things. While there are spiritual implications for this, learning how to perceive four dimensions is a concrete feature of thought. We are rapidly moving towards a future of augmented reality and Borg implants that will allow us to interact, perceive, and think directly in cyberspace, so it might be worth considering learning 4D mechanics since it will no doubt play a role in future developments.