Hong’s Cave

[I guess this extra-dimension subject is related to my previous articles on Peter Lynds and "divine" projection.]

I wondered about where those old articles I read when I was young about a three dimensional being visiting a lower dimensional world.

This somewhat inconsistent (in logical sense) mathematical fiction was supposed to be one of the first “science fiction” on dimension. This is a story about a two dimensional being, “A. Square,” having dreams about visiting a one dimensional world, and being visited by a three dimensional being to realize the “limitation” of his own world.

I can understand about its historical significance, but there are too many inconsistency that it was a bit difficult to read through. Also, a lot of the concepts it tried to describe had become relatively “fundamental” that, for me, rather the concepts, the ways to keep things consistent within the story became more interesting (for example, as long as “A. Square” was completely a two dimensional being, he wouldn’t be able to perceive the third spatial dimension).

Anyway, it was an interesting read to see where that genre of science fiction came from.

One thing reading the book made me think is that the most common conception about the time being the fourth dimension is quite absurd. As previous noted, “time” is more of a measure of changes (or highly associated with changes). Of course, it is an additional dimension. Any independent values can be one!

The thing is in a two spatial dimensional world (for that matter, any spatial dimensional worlds), the time dimension also exists. The time dimension is nothing special. So, it’s pretty weird to treat the time as the same as the other spatial dimensions and to call the space-time continuum as a four dimensional world.

It seems it’s much consistent to think of any order of spatial dimension and the time dimension as existing as a degree of changes in the states. Or something like that, I guess.

I do also understand that the dimension shouldn’t necessarily be a spatial one. Any independent values can be one. Also, it’s interesting to note that to describe what we call the three dimensional world we would definitely need many more dimensions than three.