# The Naked Scientists Forum

### Author Topic: Is space infinite?  (Read 1110 times)

#### jeannette cruse

• Guest
##### Is space infinite?
« on: 11/11/2009 08:30:02 »
jeannette cruse asked the Naked Scientists:

Hi

Is space infinite or does space only exist between two or more objects? (ie. stars planets and other matter in the universe) - in other words - if there were no objects or no universe surely by definition there would be no space?

Likewise does "space" expand as the universe expands and not exist beyond the outer boundary of the universe wherever that may be?

confused...

What do you think?

#### LeeE

• Neilep Level Member
• Posts: 3382
##### Is space infinite?
« Reply #1 on: 11/11/2009 11:51:54 »

In short though, there is infinite n-1 dimensional space within an n-dimensional environment.  What this means is that, for example, there is room for infinite area, which is two-dimensional, within a volume, which is three-dimensional, or that there is space for infinite length i.e. one-dimensional, within a two-dimensional area.

Probably the best illustration of this is a plot of the Mandlebrot set fractal:

http://en.wikipedia.org/wiki/File:Mandelset_hires.png

When you plot the Mandlebrot set you get the fractal picture shown in that link above, where the 'black' area indicates the combinations of x and y values that don't resolve, and which therefore lie in the 'set', and where the white area surrounding the black area indicates where the number pairs do resolve, and which are therefore not members of the 'set'.  As you can see, the area of the set i.e. the black area, is not infinite, but if you try to measure the length of the perimeter between the two areas you'll find that it is infinite.  We thus seem to have something that has finite area but with an infinite length perimeter (in the more colourful plots of the Mandlebrot set, the different colours just represent how many iterations are required to resolve the value pairs that fall outside the set).