I guess this is my final 'starter' question that I wish to get clear in my head with me being a newbie on the forum. How exactly do I visualise a hypercube in my head? I've seen all the nice complex imagery on the internet about it.....such as this: http://www.google.co.uk/images?hl=e...tle&resnum=6&ved=0CEMQsAQwBQ&biw=1450&bih=735 But I still can not work out in my mind how a 4th spatial dimension 'works'. I can fully understand that a 1D point can exist in a 3D world. Similarly how a 2D line can exist in a 3D world. Also a 3D shape can exist in a 3D world. I can also visualise how these entities would 'pass through' 3D worlds.....but I can not work out the 4th spatial element. How do I visualise a 4D world because these nicely animated hypercubes that I see on the internet to me seem just like 2D representations of 3D shapes that have corner points and edges that are moving. I'm sure I'm missing some vital piece of the equation that will make it become clear, but what is it? Many thanks for any help on this.