I wasn't entirely sure where to put this, but I need a concept check.
I've been bending my mind around the concept of 4 spatial dimensions and what it would mean in a gaming environment, after some thought I managed to conceive of 4 spatial dimensions, my friend got lost when I was trying to explain it so I'll try and keep it clean so you get the concept before I pose my question.
A 1D line is a series of possible states of a 0D point from the lines lower limit / start to its upper limit / end
A 2D shape is a series of possible states of a 1D line
A 3D shape a series of possible states of a 2D shape
So by extension, a 4D area is a series of possible states of a 3D shape
so if I were to take a 4D area with the 4th dimension ranging from 0 to 1. am I right in saying that if W is my 4th dimension I may accurately represent the concept of 4 spatial dimensions via Lerping 3D points between a position regarded as W of 0 and a position regarded as W of 1?
if so am I also right in saying a 4th dimension with a range exceeding 1 the 3D points would follow a curve defined by the points positions per W unit?
to my understanding these points would actually represent the shape of 3D space as opposed to the objects within 3D space, meaning an object moving at for example 10mph in W0 may in W1 be moving at 100mph and then in another location 10mph in W1 could be 100mph in W0 via relative stretching and squeezing.
I hope I didn't just confuse myself just to sound like an idiot XD
I figured the idea of 4 dimensions in which to interact would be an interesting mechanic specifically for puzzlers, but I suppose the concept in other genres would allow for interesting 4 Dimensional level design, literately adding a new depth to the game.
regarding the title about interactivity, the idea is just like WASD have you moving in X and Y, I'd imagine Q and E moving you through W, only being able to see the world in 3 dimensions it would just look like things being warped when if my concept is right it would be moving through a 4th dimension.
Thanks for reading,
Any and all informations, examples, documentation on this concept or similar concepts would be greatly appriceated.