History of the 4th Dimension

[AdamBrowne]

Hi all - this is kind of a mass mail-out I'm doing to various 4d-related sites. I came upon this site because I am writing a 17th century science fiction novel, and am looking for an account of the history of the 4th dimension. I think the idea of the fourth dimension predates Einstein (was surprised to see it being discussed in 'The Time Machine'), but by how far? Was Euclid ever inspired to look outside the box? Were there any thinkers who wrote of transdimensional matters before or during the 17th century? I like Eric Saltsman's invocation of Plato's cave, but I feel like that has less to do with geometry than Plato's notion of Forms -- which is very similar to transdimensional thinking, I guess; just not quite what I'm looking for. Also, on another discussion board, a kind user named Hugh recommended http://scholar.uwinnipeg.ca/courses/38/ ... nality.htm - but that didn't go in-depth enough.

Thanks - any help would be greatly appreciated.

[elpenmaster]

i dont know of anyone in specific who talks about the 4th dimension, but it is my opinion that people were thinking about it thousands of years ago

[Euclid]

Hi all - this is kind of a mass mail-out I'm doing to various 4d-related sites. I came upon this site because I am writing a 17th century science fiction novel, and am looking for an account of the history of the 4th dimension. I think the idea of the fourth dimension predates Einstein (was surprised to see it being discussed in 'The Time Machine'), but by how far? Was Euclid ever inspired to look outside the box? Were there any thinkers who wrote of transdimensional matters before or during the 17th century?

A quick primer:

(c), where c is a number. This is 1-D.
(x,y), where x and y are numbers identifying a point on a plane. This is 2-D.
(x,y,z),where x, y and z are numbers identifying a point in space. This is 3-D.
(x,y,z,m), where x,y,z and m are numbers identifying a point in hyperspace. In this case, 4-D.

You can go on and on with this. Where the rub comes in is trying to visualize higher than 3-space. This is what freaks everyone out. We are constrained by the physics of 3-space and the fact that our sensory systems evolved in 3-space. Remember that Euclid lived over 2,000 years ago--you will most likely only live a small fraction of that span (to put things into perspective--excuse the pun). What Euclid did with two dimensions is mind boggling. It wasn't until the late 1800's that anyone other than mathematician's began to seriously contemplate the idea of perceptually experiencing dimensions. Of course, this was Abbott's Flatland. Now we have all sorts of speculations. If I was working a sci-fi novel I would look to Riemann for inspiration.