OpenEuphoria

Re: Dimension of sequences

• Posted by Fernando Bauer <fmbauer at hot?a?l.com> Sep 15, 2007
• 611 views

Derek Parnell wrote:

Hi Derek. Thanks for your reply.

> A sequence doesn't have a 'dimension' in geometrical sense. A sequence is not
> a geometric object.

A vector or a matrix aren't geometric objects in mathematics or in programming
either, however they
have a dimension, as you know.

> Why do you need to know the 'dimension' of a sequence? I mean if you knew that
> a given sequence has a dimension of 'x', what would you use 'x' for? 
It is a theoretical question. Maybe there are rules or functions (e.g.
compression factor?) that depends on this parameter. Why do the mathematicians
and physicists calculate dimensions of fractal objects?

> 
> Are you asking the right question?
I think yes, since I understand your response as option e) (the concept does not
apply to). I don't know the answer.

> 
>  
> Fernando Bauer wrote:
> > Then, suppose you have the following sequence:
> > {
> >  {1,1,1},
> >  {1},
> >  {1,1,1}
> > }
> > 
> > If I can view this sequence as a representation of the letter "U", 
> > using your answer below, I can conclude that the dimension of this
> > sequence is 1.
> 
> This sequence has a length of 3 and a depth of 1, so in that sense it has two
> dimensions I suppose - Length and Depth. It also has a content of 7 (the
> number
> of atoms in total) so maybe a sequence has three dimensions? It also has a
> sub-sequence
> of 3, so maybe a sequence has four dimensions - Length, Depth, Content,
> Sub-sequence.
> Each of these is independant of the other so they sort of qualify as
> dimensions,
> no? But then 'Content' is kinda like 'area' in concept so maybe it doesn't
> count
> after all.
Interesting.

> 
> 
> > > > Trying to answer that question, others more basics and related to that
> > > > arise
> > > > to me (sorry if they are stupid!):
> > > > 
> > > > What is the dimension of the circumference ?
> 
> Exactly my point. The dimension of a sequence is a meaningless concept.
At least, not always, since the rectangular sequences clearly have a dimension,
like an array or matrix.

> What are you really trying to know about the sequence?

Its dimension, if there is any! :)

> 
> -- 
> Derek Parnell
> Melbourne, Australia
> Skype name: derek.j.parnell

Regards,
   Fernando