Dimensions and String

[Allmixedup]

Hi guys, I'm a newbie here and Maths isn't my forte, so please be gentle with me

 

I have been thinking that if we took a string and marked points along its length, we would describe the position of each dot according to its position with respect to the length of the string.

Yet, if we coil this up, it becomes a 2D shape, so that each point now has 2 coordinates, and similarly winding it up into a ball would give it 3 dimensions.

 

What I am getting at is that if we knew function to describe 'winding' of a line into a sphere, could we use it to condense 3 (or more)- dimensional data into a single value for the unwound string?

 

I'd really like to know whether I'm foolish for even thinking about it?!

 

Thanks Peeps!

[ajb]

I think the trouble with your picture is that the string has a finite thickness. Therefore every point on your string needs two numbers to describe it, in any given coordinate system on the string.

 

You them embed this in three dimensions and consider either the surface of the string as a 2d subspace or you consider the volume of the string as a 3d subspace.

[imatfaal]

Take a string 512 units long and carefully wind it back and forth into a box 8x8x8. You can now describe any 1x1x1 unit of the box by the position along the string (1 to 512) or the (x,y,z) coordinate (1 to 8 three times). But you will note that an 8x8x8 box will be described exactly by a max 512 pieces of information in either case - so you have saved nothing, AND you still need to explain the method of packing of your string to give a unique position.