Halo, I was reading about geometry from Tim Gowers book titled "A very brief introduction to mathematics". I came across fractional dimensions and the 4th dimension. The koch snowflake has dimension 1.2 yet he could comfortably drawn it on a 2d page (or is it complete?). Has not he just transformed the original "snowflake", scaled it, translated it, etc.. what does it have to do with dimensions? maybe, its like drawing a 3d structure on a 2d page? so this snowflake is not how it actually appears in the 1.2 dimension as drawn on 2d page? This just a extrapolation of the formulas in 1d, 2d & 3d? How do we prove such domensions exist in reality, if at all? So a 4d cube as being a cube inside a bigger cube is also for sake of visualization, like drawing a 3d cube on a 2d page? Please confirm! Danke.