# True 10D space

## Visualizing higher-dimensional space

### Perspective projection

A projection is a way of representing an N-dimensional object in a space with lower than its dimensions. For example, this flat shadow of a 3D cube on a plane is a two-dimensional perspective projection of that cube. In Hyperspace, worlds are 3-dimensional projections of up to 10-dimensional objects.

Rotating an N-dimensional object often causes its projection to warp, distort and change shape just like the shadow of this plane. So a two-dimensional being living on that plane would see the shadow as an object that arbitrarily changes shape. And that’s what the game is all about – navigating through warped space and completing objectives.

### What do projections of 10D spaces look like?

Here you see a 3D projection (or a 3D shadow if you must) of a 4D hypercube. The yellow spheres are vertices of the 3D projection. As the 4D cube rotates in 4D space, the 3D projection distorts and warps just like our 2D shadow from the example above.

# Objectives

### Starting on a two-dimensional level

Each level of Hyperspace is a simple recon mission. You start on a two-dimensional level and advance to higher dimensions as you collect artifacts. You can either collaborate with an alternate-self (Alternate) or with other players to be more efficient in collecting the artifacts. Once you are done collecting all the artifacts on a level, you can combine them together to advance to the next level.

### Three-dimensional reconnaissance

In a manner similar to the 2D world, you can collect artifacts and work together with your Alternate to collect artifacts. Just like the 2D level, you can walk to the artifacts, collect them, meet your Alternates and combine the artifacts together. You use super-membranes (the glowing lines you see here) to contact your Alternates so you always know how to find them.

### Four dimensions, Lorentz transformations and beyond

As you move to higher dimensional worlds, you play in spaces that are warped, which means the space that you see is not the same as the one seen by your alternate. So despite the ability to contact and see your Alternates, it is impossible to physically reach them as they are on a separate projection of the higher-dimensional space. This is where you use the magic of Lorentz transformations and boosts to rotate your projections to match those of your Alternate so you can find them.