Mrrl wrote:Rock, sand, grass... Whatever, but not air. You can walk by it.
gonegahgah wrote:[...]
This is because the entire volume shown is all in the same hyperhorizontal slice.
[...]
There are a few problems with the diagram because of this.
The bottom of our 3D rivers can have valleys and peaks.
Taken at non-very bottom horizontal slices these are seen as mishappen 2D slices of ridges and peaks. [...]
gonegahgah wrote:[...] Just as our 3D rivers tend to follow one preferred direction for most of their lengths with occasional splits - instead of splitting off into several different north, south, east, west or between directions all the time - I tend to believe a 4D river will tend to follow one preferred direction as well.
Generally splits occur to form forks and you would get something similar with 4D rivers.
[...] One of the cool things with 4D that you can actually touch the inside of 3D shapes.
You can't touch the inside of hypersolids but you can touch the inside of any of their hyperfaces.
So if you have a tesseract you can touch one inside of each of the 8 cube faces from the one hyperside.
[...] I must concede that the chimney hyper-riverbank provides a means to encircle the river without needing to cross it.
gonegahgah wrote:Cool. The transparent area would have to be something solid that is connected to hyperbelow or else be denser than water.
Otherwise the water above would move down to displace it and push it up.
This is because the entire volume shown is all in the same hyperhorizontal slice.
What you are representing is a 'hyperhorizontal' slice because the unseen dimension is in the down direction.
It is a cool way of thinking about it so thanks for introducing me to this perspective.
[...]
The only way to achieve something like what you have shown is via tunnelling.
Could I also ask what hyperhorizontal level of the river you are attempting to depict in your diagram?
Is it a bottom slice, a slightly off bottom slice, a middle level slice, a top slice?
Return to Higher Spatial Dimensions
Users browsing this forum: No registered users and 0 guests