Partial Dimensions - Do they exist?

[Eric Frost]

I was pondering this the other day.

Are dimensions whole numbers or is there a continuum?

We all understand one dimension is a line, two dimensions is a plane (flat surface, flat piece of paper), and three dimensions is, well 3-D.

How about something in between 1 and 2 dimensions? Say if the universe was a curved line. The curved line would break the boundaries of 1D of course because it breaks the boundary, but it's not truly 2D, because you could not access a full plane. The universe is only a curved line.

What do you think? Is there a continuum of dimensionality? Or is it always an integer? (1D, 2D, 3D, etc.)

Does breaking the 1D barrier (actually curving the line) automatically make it 2D, or do the rules of the universe requiring that you stay on the line make it something in between?

Eric

[jonfrost]

Ohh.
No idea, but its a good idea. It seems like each new dimension uses the rules of the previous dimension, but then dramatically breaks the rules. So maybe that always needs to be true. Yeah, I think maybe the 5th dimension starts with 3 dimensions that are changing over time, but then breaks the rules - maybe by warping time in regular waves? So then the 6th dimension might introduce irregular waves of time. That all requires math though to explain, so i'm just in my imagination place :-)

[Eric Frost]

I think it's a gradation. As you bend that line and it slowly becomes expanded and an actual area, then you have infinite area which should be the definition of a plane. What do you think? Do you agree there are fractional dimensions?
Eric

[evergree]

Wouldn't that still fall under the 1 dimensional category? I don't know much about it but if you have a curved line isn't that just part of a circle? Even though it is curved (such as a circle or arc) it is still just a line and there for 1 dimension, correct? I don't doubt that it is possible for there to be dimensions inside of dimensions but I don't know if these dimensions would be fractions or if they would add together to create an entirely new whole numbered dimension.

[Eric Frost]

OK, but how about two short straight lines that have an area in between. Would that not be a partial dimension? (partial plane)

Still, I think a key to to understand is -- what the rules of the universe? Can 1D only go up to a bent line or circular line or where does it flip over to 2.0? Wouldn't a line that forms a circle and (inferring an area within and outside the circle) be partially in 2D?

Granted there might be a point where it flips over sharply between being defined as 1 or 2 dimensions, but you can still imagine something in between. ?

Eric

[Eric Frost]

... then dramatically breaks the rules.

Is it so dramatic? 4D is really only animated 3D, i.e. a 3D image in motion / time. We can certainly imagine that and indeed wrap into a movie. We have achieved the fourth dimension just by creating animated 3D movies.

Eric